%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL030-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:50:37 AM UTC 2026
% Result : Unsatisfiable 140.55s 38.80s
% Output : Refutation 147.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 6
% Syntax : Number of formulae : 1546 ( 677 unt; 0 typ; 0 def)
% Number of atoms : 4478 (1678 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 20065 (2506 ~;1342 |; 0 &;16217 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 6 con; 0-2 aty)
% Number of variables : 4897 ( 0 ^;4897 !; 0 ?;4897 :)
% Comments :
%------------------------------------------------------------------------------
thf(is_a_theorem_decl,type,
is_a_theorem: $i > $o ).
thf(implies_decl,type,
implies: $i > $i > $i ).
thf(a_decl,type,
a: $i ).
thf(b_decl,type,
b: $i ).
thf(c_decl,type,
c: $i ).
thf(falsehood_decl,type,
falsehood: $i ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c0_1) ).
thf(11,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( B @ is_a_theorem )
| ~ ( A @ is_a_theorem )
| ~ ( B @ ( A @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',condensed_detachment) ).
thf(9,plain,
! [B: $i,A: $i] :
( ( B @ is_a_theorem )
| ~ ( A @ is_a_theorem )
| ~ ( B @ ( A @ implies ) @ is_a_theorem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,plain,
! [B: $i,A: $i] :
( ( B @ is_a_theorem )
| ~ ( A @ is_a_theorem )
| ~ ( B @ ( A @ implies ) @ is_a_theorem ) ),
inference(cnf,[status(esa)],[9]) ).
thf(51,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ ( D @ implies ) @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ ( D @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,10]) ).
thf(52,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ ( D @ implies ) @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[51]) ).
thf(53,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem )
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[52:[bind(A,$thf( L )),bind(B,$thf( J )),bind(C,$thf( M )),bind(D,$thf( J @ ( L @ implies ) )),bind(E,$thf( M @ ( L @ implies ) @ ( M @ ( J @ implies ) @ implies ) ))]]) ).
thf(61,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem )
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[53]) ).
thf(4,axiom,
! [B: $i,A: $i] : ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c0_2) ).
thf(12,plain,
! [B: $i,A: $i] : ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(45,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ ( C @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ ( C @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,10]) ).
thf(46,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ ( C @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[45]) ).
thf(47,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[46:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( F )),bind(D,$thf( F @ ( E @ implies ) ))]]) ).
thf(66,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[47]) ).
thf(1,negated_conjecture,
~ ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c0_6) ).
thf(7,plain,
~ ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(8,plain,
~ ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(191,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[66,8]) ).
thf(192,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[191]) ).
thf(193,plain,
~ ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[192:[bind(A,$thf( c @ ( b @ implies ) @ ( a @ implies ) )),bind(B,$thf( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) ))]]) ).
thf(262,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[66,193]) ).
thf(263,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[262]) ).
thf(264,plain,
~ ( c @ ( a @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[263:[bind(A,$thf( b @ ( a @ implies ) )),bind(B,$thf( c @ ( a @ implies ) ))]]) ).
thf(277,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[66,264]) ).
thf(278,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[277]) ).
thf(279,plain,
~ ( c @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[278:[bind(A,$thf( a )),bind(B,$thf( c ))]]) ).
thf(292,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[66,279]) ).
thf(293,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[292]) ).
thf(297,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= c )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[293]) ).
thf(573,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= c )
| ~ $true
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[61,297]) ).
thf(574,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= c )
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[573]) ).
thf(575,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( A @ implies ) )
!= c )
| ~ ( B @ ( C @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[574:[bind(A,$thf( H )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( K @ ( J @ implies ) @ ( K @ ( H @ implies ) @ implies ) ))]]) ).
thf(629,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( A @ implies ) )
!= c )
| ~ ( B @ ( C @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[575]) ).
thf(48,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ $true
| ~ ( D @ ( C @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[12,10]) ).
thf(49,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ ( D @ ( C @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[48]) ).
thf(50,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( C @ ( B @ implies ) @ ( C @ implies ) @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[49:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( H @ ( G @ implies ) @ ( H @ implies ) )),bind(D,$thf( D ))]]) ).
thf(60,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( C @ ( B @ implies ) @ ( C @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[50]) ).
thf(476,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( F @ ( E @ implies ) @ ( F @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,60]) ).
thf(477,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( F @ ( E @ implies ) @ ( F @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[476]) ).
thf(478,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[477:[bind(A,$thf( O )),bind(B,$thf( O @ ( M @ implies ) )),bind(C,$thf( P )),bind(D,$thf( P @ ( O @ implies ) @ ( P @ ( O @ ( M @ implies ) @ implies ) @ implies ) )),bind(E,$thf( M )),bind(F,$thf( O ))]]) ).
thf(487,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[478]) ).
thf(5,axiom,
! [B: $i,A: $i] : ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c0_3) ).
thf(13,plain,
! [B: $i,A: $i] : ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(39,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( C @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ ( C @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13,10]) ).
thf(40,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( C @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[39]) ).
thf(41,plain,
! [B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[40:[bind(A,$thf( F )),bind(B,$thf( H )),bind(C,$thf( F @ ( H @ ( F @ implies ) @ implies ) )),bind(D,$thf( F ))]]) ).
thf(64,plain,
! [B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[41]) ).
thf(1214,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( E @ ( D @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[487,64]) ).
thf(1215,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( E @ ( D @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[1214]) ).
thf(1216,plain,
! [A: $i] : ( A @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1215:[bind(A,$thf( C )),bind(B,$thf( C )),bind(C,$thf( C )),bind(D,$thf( C @ ( C @ implies ) )),bind(E,$thf( C ))]]) ).
thf(1241,plain,
! [A: $i] : ( A @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1216]) ).
thf(1363,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( C @ ( B @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1241,66]) ).
thf(1364,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( C @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1363]) ).
thf(1365,plain,
! [B: $i,A: $i] : ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1364:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( E @ implies ) ))]]) ).
thf(1395,plain,
! [B: $i,A: $i] : ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1365]) ).
thf(1442,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( D @ ( C @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1395,66]) ).
thf(1443,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( D @ ( C @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1442]) ).
thf(1444,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1443:[bind(A,$thf( E )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( H @ ( H @ implies ) @ ( E @ implies ) ))]]) ).
thf(1469,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1444]) ).
thf(6,axiom,
! [A: $i] : ( A @ ( falsehood @ implies ) @ is_a_theorem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c0_4) ).
thf(14,plain,
! [A: $i] : ( A @ ( falsehood @ implies ) @ is_a_theorem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(543,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ ( D @ implies ) @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ ( D @ is_a_theorem )
| ~ $true
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[61,10]) ).
thf(544,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ ( D @ implies ) @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ ( D @ is_a_theorem )
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[543]) ).
thf(545,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ is_a_theorem )
| ~ ( C @ ( A @ implies ) @ is_a_theorem )
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[544:[bind(A,$thf( F )),bind(B,$thf( H )),bind(C,$thf( I )),bind(D,$thf( I @ ( F @ implies ) )),bind(E,$thf( I @ ( H @ implies ) ))]]) ).
thf(612,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ is_a_theorem )
| ~ ( C @ ( A @ implies ) @ is_a_theorem )
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[545]) ).
thf(11439,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( C @ ( A @ implies ) @ is_a_theorem )
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[612,264]) ).
thf(11440,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) )
| ~ ( C @ ( A @ implies ) @ is_a_theorem )
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[11439]) ).
thf(11441,plain,
! [A: $i] :
( ~ ( c @ ( A @ implies ) @ is_a_theorem )
| ~ ( A @ ( a @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[11440:[bind(A,$thf( A )),bind(B,$thf( a )),bind(C,$thf( c ))]]) ).
thf(11893,plain,
! [B: $i,A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( c @ ( B @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( B @ ( a @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[14,11441]) ).
thf(11894,plain,
! [B: $i,A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( c @ ( B @ implies ) @ is_a_theorem ) )
| ~ ( B @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[11893]) ).
thf(11895,plain,
~ ( falsehood @ ( a @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[11894:[bind(A,$thf( c )),bind(B,$thf( falsehood ))]]) ).
thf(588,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) @ is_a_theorem )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[66,61]) ).
thf(589,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[588]) ).
thf(590,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[589:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(619,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[590]) ).
thf(567,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( F @ ( E @ implies ) @ ( F @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ $true
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[61,60]) ).
thf(568,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( F @ ( E @ implies ) @ ( F @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[567]) ).
thf(569,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
| ~ ( C @ ( A @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[568:[bind(A,$thf( L )),bind(B,$thf( I )),bind(C,$thf( L @ ( K @ implies ) )),bind(D,$thf( L @ ( K @ implies ) @ ( I @ implies ) )),bind(E,$thf( K )),bind(F,$thf( L ))]]) ).
thf(625,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
| ~ ( C @ ( A @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[569]) ).
thf(22673,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( C @ ( A @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[625,193]) ).
thf(22674,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ ( C @ ( A @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[22673]) ).
thf(22675,plain,
~ ( c @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[22674:[bind(A,$thf( b @ ( a @ implies ) )),bind(B,$thf( a )),bind(C,$thf( c ))]]) ).
thf(23205,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ is_a_theorem )
!= ( c @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( C @ ( A @ implies ) @ is_a_theorem )
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[612,22675]) ).
thf(23206,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ is_a_theorem )
!= ( c @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ ( C @ ( A @ implies ) @ is_a_theorem )
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[23205]) ).
thf(23207,plain,
! [A: $i] :
( ~ ( c @ ( A @ implies ) @ is_a_theorem )
| ~ ( A @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[23206:[bind(A,$thf( A )),bind(B,$thf( b @ ( a @ implies ) )),bind(C,$thf( c ))]]) ).
thf(23726,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ ( c @ ( D @ implies ) @ is_a_theorem )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[619,23207]) ).
thf(23727,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ ( c @ ( D @ implies ) @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[23726]) ).
thf(23728,plain,
! [A: $i] :
( ~ ( c @ ( b @ ( A @ implies ) @ implies ) @ is_a_theorem )
| ~ ( a @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[23727:[bind(A,$thf( E )),bind(B,$thf( a )),bind(C,$thf( b )),bind(D,$thf( b @ ( E @ implies ) ))]]) ).
thf(24120,plain,
! [A: $i] :
( ~ ( c @ ( b @ ( A @ implies ) @ implies ) @ is_a_theorem )
| ~ ( a @ is_a_theorem ) ),
inference(simp,[status(thm)],[23728]) ).
thf(25450,plain,
! [A: $i] :
( ~ $true
| ( ( c @ ( b @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ~ ( a @ is_a_theorem ) ),
inference(eqfactor_ordered,[status(thm)],[24120]) ).
thf(25531,plain,
! [A: $i] :
( ( ( c @ ( b @ ( A @ implies ) @ implies ) )
!= a )
| ~ ( a @ is_a_theorem ) ),
inference(simp,[status(thm)],[25450]) ).
thf(23162,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1241,22675]) ).
thf(23163,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[23162]) ).
thf(23255,plain,
! [A: $i] :
( ( A @ ( A @ implies ) )
!= ( c @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[23163]) ).
thf(23943,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ ( c @ ( D @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,23207]) ).
thf(23944,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ ( c @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[23943]) ).
thf(23945,plain,
! [A: $i] :
~ ( c @ ( A @ ( a @ implies ) @ ( A @ ( b @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[23944:[bind(A,$thf( a )),bind(B,$thf( b )),bind(C,$thf( J )),bind(D,$thf( J @ ( a @ implies ) @ ( J @ ( b @ implies ) @ implies ) ))]]) ).
thf(24108,plain,
! [A: $i] :
~ ( c @ ( A @ ( a @ implies ) @ ( A @ ( b @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[23945]) ).
thf(580,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) )
| ~ $true
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[61,279]) ).
thf(581,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) )
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[580]) ).
thf(608,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) )
!= c )
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[581]) ).
thf(6720,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ ( C @ implies ) @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) )
!= c )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1241,608]) ).
thf(6721,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ ( C @ implies ) @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) )
!= c ) ),
inference(simp,[status(thm)],[6720]) ).
thf(6722,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= c ),
inference(pattern_uni,[status(thm)],[6721:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(6808,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= c ),
inference(simp,[status(thm)],[6722]) ).
thf(1210,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[487,264]) ).
thf(1211,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1210]) ).
thf(1235,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[1211]) ).
thf(4183,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) )
!= c )
| ( ( C @ ( B @ ( A @ implies ) @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[1235]) ).
thf(194,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( C @ ( B @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14,66]) ).
thf(195,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( C @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[194]) ).
thf(196,plain,
! [B: $i,A: $i] : ( B @ ( falsehood @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[195:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( falsehood @ implies ) ))]]) ).
thf(207,plain,
! [B: $i,A: $i] : ( B @ ( falsehood @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[196]) ).
thf(604,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( falsehood @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[207,61]) ).
thf(605,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( falsehood @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[604]) ).
thf(606,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( A @ implies ) @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[605:[bind(A,$thf( A )),bind(B,$thf( G )),bind(C,$thf( G @ ( falsehood @ implies ) )),bind(D,$thf( A )),bind(E,$thf( E ))]]) ).
thf(628,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( A @ implies ) @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[606]) ).
thf(957,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( E @ implies ) @ is_a_theorem ) )
| ( F @ ( E @ implies ) @ ( F @ ( D @ implies ) @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[628,61]) ).
thf(958,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( E @ implies ) @ is_a_theorem ) )
| ( F @ ( E @ implies ) @ ( F @ ( D @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[957]) ).
thf(959,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( D @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ ( D @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[958:[bind(A,$thf( K )),bind(B,$thf( L )),bind(C,$thf( J )),bind(D,$thf( L @ ( K @ implies ) )),bind(E,$thf( L @ ( J @ ( falsehood @ implies ) @ implies ) )),bind(F,$thf( F ))]]) ).
thf(1021,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( D @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ ( D @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[959]) ).
thf(8968,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ ( D @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ ( F @ ( E @ implies ) @ implies ) @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1021,64]) ).
thf(8969,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ ( D @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ ( F @ ( E @ implies ) @ implies ) @ is_a_theorem ) )
| ( E @ is_a_theorem ) ),
inference(simp,[status(thm)],[8968]) ).
thf(8970,plain,
! [B: $i,A: $i] : ( A @ ( A @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[8969:[bind(A,$thf( A )),bind(B,$thf( L )),bind(C,$thf( A @ ( L @ ( falsehood @ implies ) @ implies ) )),bind(D,$thf( A )),bind(E,$thf( A @ ( A @ ( L @ ( falsehood @ implies ) @ implies ) @ implies ) )),bind(F,$thf( A ))]]) ).
thf(9036,plain,
! [B: $i,A: $i] : ( A @ ( A @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[8970]) ).
thf(9118,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9036,264]) ).
thf(9119,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[9118]) ).
thf(9185,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[9119]) ).
thf(9221,plain,
! [B: $i,A: $i] :
( ( A != c )
| ( ( A @ ( B @ ( falsehood @ implies ) @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[9185]) ).
thf(9222,plain,
! [A: $i] :
( ( c @ ( A @ ( falsehood @ implies ) @ implies ) )
!= a ),
inference(simp,[status(thm)],[9221]) ).
thf(1193,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( F @ ( E @ implies ) @ ( F @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[487,60]) ).
thf(1194,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( F @ ( E @ implies ) @ ( F @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[1193]) ).
thf(1195,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1194:[bind(A,$thf( Q )),bind(B,$thf( R )),bind(C,$thf( R @ ( Q @ implies ) @ ( O @ implies ) )),bind(D,$thf( R @ ( Q @ implies ) @ ( O @ implies ) @ ( R @ implies ) )),bind(E,$thf( O )),bind(F,$thf( R @ ( Q @ implies ) ))]]) ).
thf(1247,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1195]) ).
thf(1519,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1247,279]) ).
thf(1520,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) ),
inference(simp,[status(thm)],[1519]) ).
thf(1549,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) )
!= c ),
inference(simp,[status(thm)],[1520]) ).
thf(33,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( C @ ( B @ implies ) @ is_a_theorem ) )
| ( C @ is_a_theorem )
| ~ ( B @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14,10]) ).
thf(34,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( C @ ( B @ implies ) @ is_a_theorem ) )
| ( C @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[33]) ).
thf(35,plain,
! [A: $i] :
( ( A @ is_a_theorem )
| ~ ( falsehood @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[34:[bind(A,$thf( A )),bind(B,$thf( falsehood )),bind(C,$thf( A ))]]) ).
thf(85,plain,
! [A: $i] :
( ( ( A @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( falsehood @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[35,8]) ).
thf(86,plain,
! [A: $i] :
( ( ( A @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ ( falsehood @ is_a_theorem ) ),
inference(simp,[status(thm)],[85]) ).
thf(87,plain,
~ ( falsehood @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[86:[bind(A,$thf( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ))]]) ).
thf(189,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[66,87]) ).
thf(190,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[189]) ).
thf(206,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= falsehood )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[190]) ).
thf(419,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= falsehood )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[66,206]) ).
thf(420,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= falsehood )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[419]) ).
thf(421,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood )
| ~ ( C @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[420:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( F @ ( E @ implies ) ))]]) ).
thf(429,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[421]) ).
thf(722,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( D @ implies ) )
!= falsehood )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,429]) ).
thf(723,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( D @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[722]) ).
thf(724,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) @ ( C @ ( D @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(pattern_uni,[status(thm)],[723:[bind(A,$thf( O )),bind(B,$thf( M )),bind(C,$thf( P )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( P @ ( O @ implies ) @ ( P @ ( M @ implies ) @ implies ) @ ( M @ ( O @ implies ) @ implies ) ))]]) ).
thf(730,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) @ ( C @ ( D @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[724]) ).
thf(9116,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9036,193]) ).
thf(9117,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[9116]) ).
thf(9186,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[9117]) ).
thf(9603,plain,
! [B: $i,A: $i] :
( ( A
!= ( c @ ( a @ implies ) ) )
| ( ( A @ ( B @ ( falsehood @ implies ) @ implies ) )
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[9186]) ).
thf(9604,plain,
! [A: $i] :
( ( c @ ( a @ implies ) @ ( A @ ( falsehood @ implies ) @ implies ) )
!= ( b @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[9603]) ).
thf(197,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( D @ ( C @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,66]) ).
thf(198,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( D @ ( C @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[197]) ).
thf(199,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[198:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( H @ ( G @ implies ) @ ( H @ implies ) ))]]) ).
thf(208,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[199]) ).
thf(57,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( A @ is_a_theorem ) )
| ( B @ is_a_theorem )
| ~ ( A @ is_a_theorem ) ),
inference(eqfactor_ordered,[status(thm)],[10]) ).
thf(58,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( A @ is_a_theorem ) )
| ~ ( A @ is_a_theorem )
| ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[57]) ).
thf(523,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ~ $true
| ( E @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[208,58]) ).
thf(524,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( E @ is_a_theorem ) ),
inference(simp,[status(thm)],[523]) ).
thf(525,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ implies ) @ is_a_theorem ) )
| ( A @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[524:[bind(A,$thf( F )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( K @ ( J @ implies ) @ ( K @ implies ) @ ( F @ implies ) )),bind(E,$thf( E ))]]) ).
thf(535,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ implies ) @ is_a_theorem ) )
| ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[525]) ).
thf(9383,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ implies ) @ implies ) @ is_a_theorem )
| ( A @ is_a_theorem ) ),
inference(rewrite,[status(thm)],[535,208]) ).
thf(12011,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( a @ implies ) @ is_a_theorem ) )
| ~ ( c @ ( C @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,11441]) ).
thf(12012,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( a @ implies ) @ is_a_theorem ) )
| ~ ( c @ ( C @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[12011]) ).
thf(12013,plain,
! [A: $i] :
~ ( c @ ( a @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[12012:[bind(A,$thf( a )),bind(B,$thf( D )),bind(C,$thf( a @ ( D @ implies ) ))]]) ).
thf(12258,plain,
! [A: $i] :
~ ( c @ ( a @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[12013]) ).
thf(13302,plain,
! [B: $i,A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( c @ ( a @ ( B @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14,12258]) ).
thf(13303,plain,
! [B: $i,A: $i] :
( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( c @ ( a @ ( B @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[13302]) ).
thf(13462,plain,
! [B: $i,A: $i] :
( ( A @ ( falsehood @ implies ) )
!= ( c @ ( a @ ( B @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[13303]) ).
thf(22875,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( C @ ( A @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[625,8]) ).
thf(22876,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ ( C @ ( A @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[22875]) ).
thf(22877,plain,
~ ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[22876:[bind(A,$thf( c @ ( b @ implies ) @ ( a @ implies ) )),bind(B,$thf( b @ ( a @ implies ) )),bind(C,$thf( c @ ( a @ implies ) ))]]) ).
thf(23308,plain,
! [A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14,22877]) ).
thf(23309,plain,
! [A: $i] :
( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[23308]) ).
thf(23455,plain,
! [A: $i] :
( ( A @ ( falsehood @ implies ) )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[23309]) ).
thf(9089,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= falsehood )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9036,206]) ).
thf(9090,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[9089]) ).
thf(9091,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(pattern_uni,[status(thm)],[9090:[bind(A,$thf( F )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( F @ ( F @ ( J @ ( falsehood @ implies ) @ implies ) @ implies ) ))]]) ).
thf(9191,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[9091]) ).
thf(1409,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1395,61]) ).
thf(1410,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1409]) ).
thf(1411,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( A @ implies ) @ ( B @ ( C @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1410:[bind(A,$thf( A )),bind(B,$thf( G )),bind(C,$thf( G @ ( G @ implies ) )),bind(D,$thf( A )),bind(E,$thf( E ))]]) ).
thf(1468,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( A @ implies ) @ ( B @ ( C @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1411]) ).
thf(2307,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( C @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= falsehood )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1468,206]) ).
thf(2308,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( C @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[2307]) ).
thf(2309,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( B @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(pattern_uni,[status(thm)],[2308:[bind(A,$thf( L )),bind(B,$thf( M )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( M @ ( L @ implies ) @ ( M @ ( K @ ( K @ implies ) @ implies ) @ implies ) ))]]) ).
thf(2363,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( B @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[2309]) ).
thf(549,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13,61]) ).
thf(550,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[549]) ).
thf(551,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[550:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( G )),bind(D,$thf( G @ ( I @ ( G @ implies ) @ implies ) )),bind(E,$thf( E ))]]) ).
thf(614,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[551]) ).
thf(36,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( C @ is_a_theorem )
| ~ $true
| ~ ( C @ ( B @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[14,10]) ).
thf(37,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( C @ is_a_theorem )
| ~ ( C @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[36]) ).
thf(38,plain,
! [B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( B @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[37:[bind(A,$thf( E )),bind(B,$thf( E @ ( falsehood @ implies ) )),bind(C,$thf( C ))]]) ).
thf(62,plain,
! [B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( B @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[38]) ).
thf(3090,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( E @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[614,62]) ).
thf(3091,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( E @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[3090]) ).
thf(3092,plain,
! [B: $i,A: $i] : ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[3091:[bind(A,$thf( G )),bind(B,$thf( falsehood )),bind(C,$thf( K )),bind(D,$thf( G @ ( falsehood @ ( K @ ( falsehood @ implies ) @ implies ) @ implies ) )),bind(E,$thf( G ))]]) ).
thf(3111,plain,
! [B: $i,A: $i] : ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[3092]) ).
thf(578,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[61,264]) ).
thf(579,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) )
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[578]) ).
thf(610,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) ) )
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[579]) ).
thf(11064,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3111,610]) ).
thf(11065,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[11064]) ).
thf(11066,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( falsehood @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(pattern_uni,[status(thm)],[11065:[bind(A,$thf( A )),bind(B,$thf( I )),bind(C,$thf( A )),bind(D,$thf( falsehood @ ( I @ ( falsehood @ implies ) @ implies ) )),bind(E,$thf( E ))]]) ).
thf(11175,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( falsehood @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[11066]) ).
thf(6747,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) )
!= c )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[66,608]) ).
thf(6748,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) )
!= c )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[6747]) ).
thf(6749,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) )
!= c )
| ~ ( B @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[6748:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(6830,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) )
!= c )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[6749]) ).
thf(447,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= c )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[66,297]) ).
thf(448,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= c )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[447]) ).
thf(449,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) )
!= c )
| ~ ( C @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[448:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( F @ ( E @ implies ) ))]]) ).
thf(456,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) )
!= c )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[449]) ).
thf(838,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= c )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13,456]) ).
thf(839,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= c ) ),
inference(simp,[status(thm)],[838]) ).
thf(840,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ ( C @ implies ) @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= c ),
inference(pattern_uni,[status(thm)],[839:[bind(A,$thf( G )),bind(B,$thf( K )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( G @ ( G @ ( K @ ( G @ implies ) @ implies ) @ implies ) ))]]) ).
thf(873,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ ( C @ implies ) @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= c ),
inference(simp,[status(thm)],[840]) ).
thf(26,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,8]) ).
thf(27,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[26]) ).
thf(28,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[27]) ).
thf(110,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) ) )
| ( ( B @ ( A @ implies ) )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[28]) ).
thf(112,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) )
!= ( c @ ( a @ implies ) ) )
| ( ( C @ ( B @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( B @ ( A @ implies ) )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[110]) ).
thf(1736,plain,
! [C: $i,B: $i,A: $i] :
( ( ( b @ ( a @ implies ) )
!= ( B @ ( A @ implies ) ) )
| ( ( C @ ( B @ implies ) )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ( ( C @ ( A @ implies ) )
!= ( c @ ( a @ implies ) ) )
| ( ( B @ ( A @ implies ) )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[112]) ).
thf(1811,plain,
! [C: $i,B: $i,A: $i] :
( ( b != B )
| ( a != A )
| ( ( C @ ( B @ implies ) )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ( C != c )
| ( A != a )
| ( ( B @ ( A @ implies ) )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[1736]) ).
thf(1836,plain,
( ( ( c @ ( b @ implies ) @ ( a @ implies ) )
!= ( c @ ( b @ implies ) ) )
| ( ( c @ ( b @ implies ) @ ( a @ implies ) )
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[1811]) ).
thf(2994,plain,
( ( ( c @ ( b @ implies ) @ ( a @ implies ) )
!= ( c @ ( b @ implies ) ) )
| ( ( c @ ( b @ implies ) )
!= b )
| ( a != a ) ),
inference(simp,[status(thm)],[1836]) ).
thf(3012,plain,
( ( ( c @ ( b @ implies ) @ ( a @ implies ) )
!= ( c @ ( b @ implies ) ) )
| ( ( c @ ( b @ implies ) )
!= b ) ),
inference(simp,[status(thm)],[2994]) ).
thf(265,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,193]) ).
thf(266,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[265]) ).
thf(269,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[266]) ).
thf(9120,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9036,279]) ).
thf(9121,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) ),
inference(simp,[status(thm)],[9120]) ).
thf(9184,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) )
!= c ),
inference(simp,[status(thm)],[9121]) ).
thf(1494,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( D @ ( E @ implies ) @ is_a_theorem ) )
| ( F @ ( E @ implies ) @ ( F @ ( D @ implies ) @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1247,61]) ).
thf(1495,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( D @ ( E @ implies ) @ is_a_theorem ) )
| ( F @ ( E @ implies ) @ ( F @ ( D @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1494]) ).
thf(1496,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( D @ implies ) @ ( A @ ( D @ ( C @ implies ) @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1495:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( J )),bind(D,$thf( J @ ( I @ implies ) @ ( G @ implies ) )),bind(E,$thf( J )),bind(F,$thf( F ))]]) ).
thf(1561,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( D @ implies ) @ ( A @ ( D @ ( C @ implies ) @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1496]) ).
thf(4830,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ implies ) @ ( A @ ( D @ ( C @ implies ) @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ ( G @ ( F @ implies ) @ ( G @ implies ) @ implies ) @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1561,60]) ).
thf(4831,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ implies ) @ ( A @ ( D @ ( C @ implies ) @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ ( G @ ( F @ implies ) @ ( G @ implies ) @ implies ) @ is_a_theorem ) )
| ( E @ is_a_theorem ) ),
inference(simp,[status(thm)],[4830]) ).
thf(4832,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( D @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[4831:[bind(A,$thf( Y @ ( X @ implies ) @ ( V @ implies ) @ ( T @ implies ) )),bind(B,$thf( V )),bind(C,$thf( X )),bind(D,$thf( Y )),bind(E,$thf( Y @ ( X @ implies ) @ ( V @ implies ) @ ( T @ implies ) @ ( Y @ implies ) )),bind(F,$thf( T )),bind(G,$thf( Y @ ( X @ implies ) @ ( V @ implies ) ))]]) ).
thf(4911,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( D @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[4832]) ).
thf(5067,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( D @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4911,264]) ).
thf(5068,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( D @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[5067]) ).
thf(5112,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( D @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[5068]) ).
thf(5564,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= c )
| ( D != a ) ),
inference(simp,[status(thm)],[5112]) ).
thf(5565,plain,
! [C: $i,B: $i,A: $i] :
( ( a @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= c ),
inference(simp,[status(thm)],[5564]) ).
thf(23872,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ ( c @ ( C @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,23207]) ).
thf(23873,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ ( c @ ( C @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[23872]) ).
thf(23874,plain,
! [A: $i] :
~ ( c @ ( b @ ( a @ implies ) @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[23873:[bind(A,$thf( b @ ( a @ implies ) )),bind(B,$thf( F )),bind(C,$thf( b @ ( a @ implies ) @ ( F @ implies ) ))]]) ).
thf(24098,plain,
! [A: $i] :
~ ( c @ ( b @ ( a @ implies ) @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[23874]) ).
thf(24609,plain,
! [B: $i,A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( c @ ( b @ ( a @ implies ) @ ( B @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14,24098]) ).
thf(24610,plain,
! [B: $i,A: $i] :
( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( c @ ( b @ ( a @ implies ) @ ( B @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[24609]) ).
thf(24758,plain,
! [B: $i,A: $i] :
( ( A @ ( falsehood @ implies ) )
!= ( c @ ( b @ ( a @ implies ) @ ( B @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[24610]) ).
thf(27682,plain,
! [B: $i,A: $i] :
( ( A != c )
| ( ( b @ ( a @ implies ) @ ( B @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[24758]) ).
thf(27683,plain,
! [A: $i] :
( ( b @ ( a @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[27682]) ).
thf(975,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[628,193]) ).
thf(976,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[975]) ).
thf(1003,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[976]) ).
thf(4782,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( c @ ( a @ implies ) ) )
| ( ( B @ ( C @ ( falsehood @ implies ) @ implies ) )
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[1003]) ).
thf(8729,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( falsehood @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) ) )
| ( ( B @ ( A @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( B @ ( C @ ( falsehood @ implies ) @ implies ) )
!= ( b @ ( a @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[4782]) ).
thf(8739,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( falsehood @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) ) )
| ( B != b )
| ( A != a )
| ( B != b )
| ( ( C @ ( falsehood @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[8729]) ).
thf(8747,plain,
! [A: $i] :
( ( ( b @ ( A @ ( falsehood @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) ) )
| ( ( A @ ( falsehood @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[8739]) ).
thf(1526,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1247,66]) ).
thf(1527,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1526]) ).
thf(1528,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ implies ) @ ( B @ implies ) @ ( D @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1527:[bind(A,$thf( H )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( K @ ( J @ implies ) @ ( H @ implies ) @ ( K @ implies ) ))]]) ).
thf(1562,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ implies ) @ ( B @ implies ) @ ( D @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1528]) ).
thf(2416,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( D @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( F @ ( E @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1562,66]) ).
thf(2417,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( D @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( F @ ( E @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[2416]) ).
thf(2418,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( E @ ( D @ implies ) @ ( C @ implies ) @ ( E @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2417:[bind(A,$thf( G )),bind(B,$thf( K )),bind(C,$thf( M )),bind(D,$thf( N )),bind(E,$thf( E )),bind(F,$thf( N @ ( M @ implies ) @ ( K @ implies ) @ ( N @ implies ) @ ( G @ implies ) ))]]) ).
thf(2448,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( E @ ( D @ implies ) @ ( C @ implies ) @ ( E @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[2418]) ).
thf(594,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) )
| ~ $true
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[61,87]) ).
thf(595,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) )
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[594]) ).
thf(611,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) )
!= falsehood )
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[595]) ).
thf(7236,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) )
!= falsehood )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3111,611]) ).
thf(7237,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[7236]) ).
thf(7238,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( falsehood @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= falsehood ),
inference(pattern_uni,[status(thm)],[7237:[bind(A,$thf( A )),bind(B,$thf( I )),bind(C,$thf( A )),bind(D,$thf( falsehood @ ( I @ ( falsehood @ implies ) @ implies ) )),bind(E,$thf( E ))]]) ).
thf(7345,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( falsehood @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[7238]) ).
thf(576,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[61,193]) ).
thf(577,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[576]) ).
thf(609,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) ) )
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[577]) ).
thf(10788,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ ( C @ implies ) @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1241,609]) ).
thf(10789,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ ( C @ implies ) @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[10788]) ).
thf(10790,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(pattern_uni,[status(thm)],[10789:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(10894,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[10790]) ).
thf(10940,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( c @ ( a @ implies ) ) )
| ( ( B @ ( A @ implies ) )
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[10894]) ).
thf(2336,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( C @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1468,66]) ).
thf(2337,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( C @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[2336]) ).
thf(2338,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ implies ) @ ( D @ ( B @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2337:[bind(A,$thf( L )),bind(B,$thf( M )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( M @ ( L @ implies ) @ ( M @ ( K @ ( K @ implies ) @ implies ) @ implies ) ))]]) ).
thf(2362,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ implies ) @ ( D @ ( B @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[2338]) ).
thf(42,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ $true
| ~ ( D @ ( C @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[13,10]) ).
thf(43,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ ( D @ ( C @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[42]) ).
thf(44,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( B @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[43:[bind(A,$thf( F )),bind(B,$thf( J )),bind(C,$thf( F @ ( F @ ( J @ ( F @ implies ) @ implies ) @ implies ) )),bind(D,$thf( D ))]]) ).
thf(65,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( B @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[44]) ).
thf(5823,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( D @ ( B @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ ( F @ ( F @ ( G @ ( F @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2362,65]) ).
thf(5824,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( D @ ( B @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ ( F @ ( F @ ( G @ ( F @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( E @ is_a_theorem ) ),
inference(simp,[status(thm)],[5823]) ).
thf(5825,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ implies ) @ ( C @ ( A @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[5824:[bind(A,$thf( I @ ( I @ ( M @ ( I @ implies ) @ implies ) @ implies ) )),bind(B,$thf( S )),bind(C,$thf( T )),bind(D,$thf( U )),bind(E,$thf( U @ ( T @ implies ) @ ( U @ ( S @ ( S @ implies ) @ implies ) @ implies ) )),bind(F,$thf( I )),bind(G,$thf( M ))]]) ).
thf(5885,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ implies ) @ ( C @ ( A @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[5825]) ).
thf(6160,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5885,264]) ).
thf(6161,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[6160]) ).
thf(6208,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ ( A @ implies ) @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[6161]) ).
thf(6241,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) )
!= c )
| ( ( C @ ( A @ ( A @ implies ) @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[6208]) ).
thf(23783,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( C @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( C @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[9036,23207]) ).
thf(23784,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( C @ implies ) @ is_a_theorem ) )
| ~ ( C @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[23783]) ).
thf(23785,plain,
! [A: $i] :
~ ( c @ ( A @ ( falsehood @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[23784:[bind(A,$thf( c )),bind(B,$thf( G )),bind(C,$thf( c @ ( G @ ( falsehood @ implies ) @ implies ) ))]]) ).
thf(24134,plain,
! [A: $i] :
~ ( c @ ( A @ ( falsehood @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[23785]) ).
thf(12354,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ is_a_theorem )
!= ( falsehood @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( C @ ( A @ implies ) @ is_a_theorem )
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[612,11895]) ).
thf(12355,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ is_a_theorem )
!= ( falsehood @ ( a @ implies ) @ is_a_theorem ) )
| ~ ( C @ ( A @ implies ) @ is_a_theorem )
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[12354]) ).
thf(12356,plain,
! [A: $i] :
( ~ ( falsehood @ ( A @ implies ) @ is_a_theorem )
| ~ ( A @ ( a @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[12355:[bind(A,$thf( A )),bind(B,$thf( a )),bind(C,$thf( falsehood ))]]) ).
thf(16101,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( a @ implies ) @ is_a_theorem ) )
| ~ ( falsehood @ ( C @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1395,12356]) ).
thf(16102,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( a @ implies ) @ is_a_theorem ) )
| ~ ( falsehood @ ( C @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[16101]) ).
thf(16103,plain,
! [A: $i] :
~ ( falsehood @ ( A @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[16102:[bind(A,$thf( a )),bind(B,$thf( E )),bind(C,$thf( E @ ( E @ implies ) ))]]) ).
thf(16236,plain,
! [A: $i] :
~ ( falsehood @ ( A @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[16103]) ).
thf(2328,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( C @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1468,279]) ).
thf(2329,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( C @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) ),
inference(simp,[status(thm)],[2328]) ).
thf(2360,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( C @ ( C @ implies ) @ implies ) @ implies ) )
!= c ),
inference(simp,[status(thm)],[2329]) ).
thf(8725,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( c @ ( a @ implies ) ) )
| ( B != b )
| ( ( C @ ( falsehood @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[4782]) ).
thf(8752,plain,
! [B: $i,A: $i] :
( ( ( b @ ( A @ implies ) )
!= ( c @ ( a @ implies ) ) )
| ( ( B @ ( falsehood @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[8725]) ).
thf(315,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( falsehood @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( D @ ( C @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[207,66]) ).
thf(316,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( falsehood @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( D @ ( C @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[315]) ).
thf(317,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[316:[bind(A,$thf( E )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( H @ ( falsehood @ implies ) @ ( E @ implies ) ))]]) ).
thf(334,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[317]) ).
thf(59,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= A )
| ~ ( A @ is_a_theorem )
| ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[57]) ).
thf(374,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= D )
| ~ $true
| ( E @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[334,59]) ).
thf(375,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= D )
| ( E @ is_a_theorem ) ),
inference(simp,[status(thm)],[374]) ).
thf(376,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ implies ) )
!= ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ ( B @ implies ) ) )
| ( A @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[375:[bind(A,$thf( F )),bind(B,$thf( H )),bind(C,$thf( K )),bind(D,$thf( K @ ( falsehood @ implies ) @ ( H @ implies ) @ ( F @ implies ) )),bind(E,$thf( E ))]]) ).
thf(404,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ implies ) )
!= ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ ( B @ implies ) ) )
| ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[376]) ).
thf(11979,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( C @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( C @ ( a @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[13,11441]) ).
thf(11980,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( C @ implies ) @ is_a_theorem ) )
| ~ ( C @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[11979]) ).
thf(11981,plain,
! [A: $i] :
~ ( c @ ( A @ ( c @ implies ) @ implies ) @ ( a @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[11980:[bind(A,$thf( c )),bind(B,$thf( G )),bind(C,$thf( c @ ( G @ ( c @ implies ) @ implies ) ))]]) ).
thf(12254,plain,
! [A: $i] :
~ ( c @ ( A @ ( c @ implies ) @ implies ) @ ( a @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[11981]) ).
thf(13729,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( C @ ( c @ implies ) @ implies ) @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[66,12254]) ).
thf(13730,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( C @ ( c @ implies ) @ implies ) @ ( a @ implies ) @ is_a_theorem ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[13729]) ).
thf(13731,plain,
! [A: $i] :
~ ( c @ ( A @ ( c @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[13730:[bind(A,$thf( a )),bind(B,$thf( c @ ( G @ ( c @ implies ) @ implies ) )),bind(C,$thf( G ))]]) ).
thf(13835,plain,
! [A: $i] :
~ ( c @ ( A @ ( c @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[13731]) ).
thf(13849,plain,
! [B: $i,A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( c @ ( B @ ( c @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14,13835]) ).
thf(13850,plain,
! [B: $i,A: $i] :
( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( c @ ( B @ ( c @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[13849]) ).
thf(13975,plain,
! [B: $i,A: $i] :
( ( A @ ( falsehood @ implies ) )
!= ( c @ ( B @ ( c @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[13850]) ).
thf(977,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[628,264]) ).
thf(978,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[977]) ).
thf(1006,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[978]) ).
thf(2216,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= c )
| ( ( B @ ( C @ ( falsehood @ implies ) @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[1006]) ).
thf(1217,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[487,66]) ).
thf(1218,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1217]) ).
thf(1219,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ implies ) @ ( D @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1218:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( D )),bind(E,$thf( M @ ( L @ implies ) @ ( M @ ( L @ ( J @ implies ) @ implies ) @ implies ) ))]]) ).
thf(1243,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ implies ) @ ( D @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1219]) ).
thf(1349,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) @ ( B @ implies ) )
!= c )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1241,456]) ).
thf(1350,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) @ ( B @ implies ) )
!= c ) ),
inference(simp,[status(thm)],[1349]) ).
thf(1351,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= c ),
inference(pattern_uni,[status(thm)],[1350:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( F @ ( F @ implies ) ))]]) ).
thf(1391,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= c ),
inference(simp,[status(thm)],[1351]) ).
thf(12107,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( falsehood @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( a @ implies ) @ is_a_theorem ) )
| ~ ( c @ ( C @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[207,11441]) ).
thf(12108,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( falsehood @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( a @ implies ) @ is_a_theorem ) )
| ~ ( c @ ( C @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[12107]) ).
thf(12109,plain,
! [A: $i] :
~ ( c @ ( A @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[12108:[bind(A,$thf( a )),bind(B,$thf( E )),bind(C,$thf( E @ ( falsehood @ implies ) ))]]) ).
thf(12231,plain,
! [A: $i] :
~ ( c @ ( A @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[12109]) ).
thf(12685,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( B @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1241,12231]) ).
thf(12686,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( B @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[12685]) ).
thf(12763,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( c @ ( B @ ( falsehood @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[12686]) ).
thf(12004,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( C @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( C @ ( a @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[3111,11441]) ).
thf(12005,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( C @ implies ) @ is_a_theorem ) )
| ~ ( C @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[12004]) ).
thf(12006,plain,
! [A: $i] :
~ ( falsehood @ ( A @ ( falsehood @ implies ) @ implies ) @ ( a @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[12005:[bind(A,$thf( c )),bind(B,$thf( G )),bind(C,$thf( falsehood @ ( G @ ( falsehood @ implies ) @ implies ) ))]]) ).
thf(12257,plain,
! [A: $i] :
~ ( falsehood @ ( A @ ( falsehood @ implies ) @ implies ) @ ( a @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[12006]) ).
thf(23766,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ ( c @ ( D @ implies ) @ is_a_theorem )
| ~ $true
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[61,23207]) ).
thf(23767,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ ( c @ ( D @ implies ) @ is_a_theorem )
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[23766]) ).
thf(23768,plain,
! [A: $i] :
( ~ ( c @ ( b @ ( A @ implies ) @ implies ) @ is_a_theorem )
| ~ ( a @ ( A @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[23767:[bind(A,$thf( a )),bind(B,$thf( E )),bind(C,$thf( b )),bind(D,$thf( b @ ( E @ implies ) ))]]) ).
thf(24131,plain,
! [A: $i] :
( ~ ( c @ ( b @ ( A @ implies ) @ implies ) @ is_a_theorem )
| ~ ( a @ ( A @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[23768]) ).
thf(1729,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) )
!= ( c @ ( a @ implies ) ) )
| ( C != b )
| ( B != a )
| ( ( B @ ( A @ implies ) )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[112]) ).
thf(1843,plain,
! [A: $i] :
( ( ( b @ ( A @ implies ) )
!= ( c @ ( a @ implies ) ) )
| ( ( a @ ( A @ implies ) )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[1729]) ).
thf(5247,plain,
! [A: $i] :
( ( ( c @ ( a @ implies ) )
!= ( a @ ( A @ implies ) ) )
| ( ( b @ ( A @ implies ) )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ( ( a @ ( A @ implies ) )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[1843]) ).
thf(5255,plain,
! [A: $i] :
( ( ( c @ ( a @ implies ) )
!= ( a @ ( A @ implies ) ) )
| ( ( b @ ( A @ implies ) )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ( ( c @ ( b @ implies ) )
!= a )
| ( A != a ) ),
inference(simp,[status(thm)],[5247]) ).
thf(5269,plain,
( ( ( c @ ( a @ implies ) )
!= ( a @ ( a @ implies ) ) )
| ( ( c @ ( b @ implies ) @ ( a @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( c @ ( b @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[5255]) ).
thf(17,plain,
! [A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14,8]) ).
thf(18,plain,
! [A: $i] :
( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[17]) ).
thf(20,plain,
! [A: $i] :
( ( A @ ( falsehood @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[18]) ).
thf(24,plain,
! [A: $i] :
( ( A
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) ) )
| ( ( c @ ( b @ implies ) @ ( a @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[20]) ).
thf(25,plain,
( ( c @ ( b @ implies ) @ ( a @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[24]) ).
thf(16013,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( a @ implies ) @ is_a_theorem ) )
| ~ ( falsehood @ ( C @ implies ) @ is_a_theorem )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[66,12356]) ).
thf(16014,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( a @ implies ) @ is_a_theorem ) )
| ~ ( falsehood @ ( C @ implies ) @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[16013]) ).
thf(16015,plain,
! [A: $i] :
( ~ ( falsehood @ ( A @ implies ) @ is_a_theorem )
| ~ ( A @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[16014:[bind(A,$thf( a )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(16221,plain,
! [A: $i] :
( ~ ( falsehood @ ( A @ implies ) @ is_a_theorem )
| ~ ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[16015]) ).
thf(17424,plain,
! [A: $i] :
( ~ $true
| ( ( falsehood @ ( A @ implies ) @ is_a_theorem )
!= ( A @ is_a_theorem ) )
| ~ ( A @ is_a_theorem ) ),
inference(eqfactor_ordered,[status(thm)],[16221]) ).
thf(17428,plain,
! [A: $i] :
( ( ( falsehood @ ( A @ implies ) )
!= A )
| ~ ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[17424]) ).
thf(1352,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1241,193]) ).
thf(1353,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1352]) ).
thf(1386,plain,
! [A: $i] :
( ( A @ ( A @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[1353]) ).
thf(516,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[208,66]) ).
thf(517,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[516]) ).
thf(518,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[517:[bind(A,$thf( F )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( K @ ( J @ implies ) @ ( K @ implies ) @ ( F @ implies ) ))]]) ).
thf(534,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[518]) ).
thf(1688,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( F @ ( E @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[534,66]) ).
thf(1689,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( F @ ( E @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1688]) ).
thf(1690,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( E @ ( D @ implies ) @ ( E @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1689:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( M )),bind(D,$thf( N )),bind(E,$thf( E )),bind(F,$thf( N @ ( M @ implies ) @ ( N @ implies ) @ ( I @ implies ) @ ( G @ implies ) ))]]) ).
thf(1724,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( E @ ( D @ implies ) @ ( E @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1690]) ).
thf(7230,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ ( C @ implies ) @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) )
!= falsehood )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1241,611]) ).
thf(7231,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ ( C @ implies ) @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[7230]) ).
thf(7232,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= falsehood ),
inference(pattern_uni,[status(thm)],[7231:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(7343,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[7232]) ).
thf(23338,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( C @ ( A @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[625,22877]) ).
thf(23339,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ ( C @ ( A @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[23338]) ).
thf(23340,plain,
~ ( c @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[23339:[bind(A,$thf( c @ ( b @ implies ) @ ( a @ implies ) )),bind(B,$thf( a )),bind(C,$thf( c ))]]) ).
thf(3125,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= falsehood )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3111,206]) ).
thf(3126,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[3125]) ).
thf(3127,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( falsehood @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(pattern_uni,[status(thm)],[3126:[bind(A,$thf( F )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( F @ ( falsehood @ ( J @ ( falsehood @ implies ) @ implies ) @ implies ) ))]]) ).
thf(3195,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( falsehood @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[3127]) ).
thf(14092,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ ( C @ ( falsehood @ implies ) @ implies ) @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[66,12257]) ).
thf(14093,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ ( C @ ( falsehood @ implies ) @ implies ) @ ( a @ implies ) @ is_a_theorem ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[14092]) ).
thf(14094,plain,
! [A: $i] :
~ ( falsehood @ ( A @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[14093:[bind(A,$thf( a )),bind(B,$thf( falsehood @ ( G @ ( falsehood @ implies ) @ implies ) )),bind(C,$thf( G ))]]) ).
thf(14198,plain,
! [A: $i] :
~ ( falsehood @ ( A @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[14094]) ).
thf(14257,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1241,14198]) ).
thf(14258,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[14257]) ).
thf(14351,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[14258]) ).
thf(8726,plain,
! [C: $i,B: $i,A: $i] :
( ( B != c )
| ( A != a )
| ( ( B @ ( C @ ( falsehood @ implies ) @ implies ) )
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[4782]) ).
thf(8753,plain,
! [A: $i] :
( ( c @ ( A @ ( falsehood @ implies ) @ implies ) )
!= ( b @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[8726]) ).
thf(507,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= c )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[208,297]) ).
thf(508,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= c ) ),
inference(simp,[status(thm)],[507]) ).
thf(509,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= c ),
inference(pattern_uni,[status(thm)],[508:[bind(A,$thf( F )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( K @ ( J @ implies ) @ ( K @ implies ) @ ( F @ implies ) ))]]) ).
thf(542,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= c ),
inference(simp,[status(thm)],[509]) ).
thf(1599,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1469,264]) ).
thf(1600,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1599]) ).
thf(1628,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[1600]) ).
thf(1678,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[534,264]) ).
thf(1679,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1678]) ).
thf(1709,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[1679]) ).
thf(260,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,193]) ).
thf(261,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[260]) ).
thf(268,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[261]) ).
thf(914,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) )
!= ( c @ ( a @ implies ) ) )
| ( A
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[268]) ).
thf(915,plain,
! [A: $i] :
( ( b @ ( a @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[914]) ).
thf(916,plain,
! [A: $i] :
( ( ( b @ ( a @ implies ) )
!= c )
| ( A != a ) ),
inference(simp,[status(thm)],[915]) ).
thf(917,plain,
( ( b @ ( a @ implies ) )
!= c ),
inference(simp,[status(thm)],[916]) ).
thf(3042,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( F @ ( E @ implies ) @ ( F @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[614,60]) ).
thf(3043,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( F @ ( E @ implies ) @ ( F @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[3042]) ).
thf(3044,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ implies ) @ ( C @ ( A @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[3043:[bind(A,$thf( P @ ( O @ implies ) )),bind(B,$thf( P )),bind(C,$thf( N )),bind(D,$thf( P @ ( O @ implies ) @ ( P @ ( N @ ( P @ implies ) @ implies ) @ implies ) )),bind(E,$thf( O )),bind(F,$thf( P ))]]) ).
thf(3101,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ implies ) @ ( C @ ( A @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[3044]) ).
thf(3445,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3101,66]) ).
thf(3446,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[3445]) ).
thf(3447,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ implies ) @ ( D @ ( B @ ( D @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[3446:[bind(A,$thf( K )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( D )),bind(E,$thf( M @ ( L @ implies ) @ ( M @ ( K @ ( M @ implies ) @ implies ) @ implies ) ))]]) ).
thf(3485,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ implies ) @ ( D @ ( B @ ( D @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[3447]) ).
thf(256,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13,193]) ).
thf(257,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[256]) ).
thf(267,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[257]) ).
thf(2895,plain,
! [B: $i,A: $i] :
( ( A
!= ( c @ ( a @ implies ) ) )
| ( ( A @ ( B @ ( A @ implies ) @ implies ) )
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[267]) ).
thf(2896,plain,
! [A: $i] :
( ( c @ ( a @ implies ) @ ( A @ ( c @ ( a @ implies ) @ implies ) @ implies ) )
!= ( b @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[2895]) ).
thf(2897,plain,
! [A: $i] :
( ( ( c @ ( a @ implies ) )
!= b )
| ( ( A @ ( c @ ( a @ implies ) @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[2896]) ).
thf(353,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( falsehood @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= C )
| ~ $true
| ( D @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[207,59]) ).
thf(354,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( falsehood @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= C )
| ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[353]) ).
thf(355,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ implies ) )
!= ( C @ ( falsehood @ implies ) @ ( B @ implies ) ) )
| ( A @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[354:[bind(A,$thf( E )),bind(B,$thf( H )),bind(C,$thf( H @ ( falsehood @ implies ) @ ( E @ implies ) )),bind(D,$thf( D ))]]) ).
thf(357,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ implies ) )
!= ( C @ ( falsehood @ implies ) @ ( B @ implies ) ) )
| ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[355]) ).
thf(1430,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1395,193]) ).
thf(1431,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1430]) ).
thf(1462,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[1431]) ).
thf(1517,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1247,264]) ).
thf(1518,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1517]) ).
thf(1545,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[1518]) ).
thf(3156,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( D @ ( C @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3111,66]) ).
thf(3157,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( D @ ( C @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[3156]) ).
thf(3158,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( falsehood @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[3157:[bind(A,$thf( F )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( F @ ( falsehood @ ( J @ ( falsehood @ implies ) @ implies ) @ implies ) ))]]) ).
thf(3194,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( falsehood @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[3158]) ).
thf(3243,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( falsehood @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3194,66]) ).
thf(3244,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( falsehood @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[3243]) ).
thf(3245,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( C @ ( falsehood @ ( D @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[3244:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( M )),bind(D,$thf( D )),bind(E,$thf( I @ ( falsehood @ ( M @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( F @ implies ) ))]]) ).
thf(3277,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( C @ ( falsehood @ ( D @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[3245]) ).
thf(3350,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( falsehood @ ( D @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3277,264]) ).
thf(3351,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( falsehood @ ( D @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[3350]) ).
thf(3385,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( falsehood @ ( D @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[3351]) ).
thf(1427,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= c )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1395,456]) ).
thf(1428,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= c ) ),
inference(simp,[status(thm)],[1427]) ).
thf(1429,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= c ),
inference(pattern_uni,[status(thm)],[1428:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( I @ ( I @ implies ) @ ( F @ implies ) ))]]) ).
thf(1479,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= c ),
inference(simp,[status(thm)],[1429]) ).
thf(115,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) )
!= ( B @ ( A @ implies ) ) )
| ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ( ( B @ ( A @ implies ) )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[110]) ).
thf(117,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) )
!= ( B @ ( A @ implies ) ) )
| ( ( C @ ( A @ implies ) )
!= ( c @ ( b @ implies ) ) )
| ( ( C @ ( B @ implies ) )
!= a )
| ( ( B @ ( A @ implies ) )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[115]) ).
thf(1909,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c @ ( a @ implies ) )
!= B )
| ( ( b @ ( a @ implies ) )
!= A )
| ( C != c )
| ( A != b )
| ( ( C @ ( B @ implies ) )
!= a )
| ( ( B @ ( A @ implies ) )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[117]) ).
thf(2081,plain,
( ( ( b @ ( a @ implies ) )
!= b )
| ( ( c @ ( c @ ( a @ implies ) @ implies ) )
!= a )
| ( ( c @ ( a @ implies ) @ ( b @ implies ) )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[1909]) ).
thf(10473,plain,
( ( ( b @ ( a @ implies ) )
!= b )
| ( ( c @ ( c @ ( a @ implies ) @ implies ) )
!= a )
| ( ( c @ ( b @ implies ) )
!= ( c @ ( a @ implies ) ) )
| ( b != a ) ),
inference(simp,[status(thm)],[2081]) ).
thf(10944,plain,
( ( ( b @ ( a @ implies ) )
!= b )
| ( ( c @ ( c @ ( a @ implies ) @ implies ) )
!= a )
| ( c != c )
| ( b != a )
| ( b != a ) ),
inference(simp,[status(thm)],[10473]) ).
thf(10945,plain,
( ( ( b @ ( a @ implies ) )
!= b )
| ( ( c @ ( c @ ( a @ implies ) @ implies ) )
!= a )
| ( b != a ) ),
inference(simp,[status(thm)],[10944]) ).
thf(3144,plain,
! [B: $i,A: $i] :
( ( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3111,193]) ).
thf(3145,plain,
! [B: $i,A: $i] :
( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[3144]) ).
thf(3180,plain,
! [B: $i,A: $i] :
( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[3145]) ).
thf(3233,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( falsehood @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3194,264]) ).
thf(3234,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( falsehood @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[3233]) ).
thf(3268,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( falsehood @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[3234]) ).
thf(14213,plain,
! [B: $i,A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14,14198]) ).
thf(14214,plain,
! [B: $i,A: $i] :
( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[14213]) ).
thf(14376,plain,
! [B: $i,A: $i] :
( ( A @ ( falsehood @ implies ) )
!= ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[14214]) ).
thf(984,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[628,66]) ).
thf(985,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[984]) ).
thf(986,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ implies ) @ ( D @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[985:[bind(A,$thf( L )),bind(B,$thf( M )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( M @ ( L @ implies ) @ ( M @ ( K @ ( falsehood @ implies ) @ implies ) @ implies ) ))]]) ).
thf(1018,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ implies ) @ ( D @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[986]) ).
thf(2932,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( D @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1018,264]) ).
thf(2933,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[2932]) ).
thf(2964,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[2933]) ).
thf(4787,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( D @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) )
!= c )
| ( A != a ) ),
inference(simp,[status(thm)],[2964]) ).
thf(4788,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ ( falsehood @ implies ) @ implies ) @ implies ) )
!= c ),
inference(simp,[status(thm)],[4787]) ).
thf(969,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= c )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[628,297]) ).
thf(970,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= c ) ),
inference(simp,[status(thm)],[969]) ).
thf(971,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= c ),
inference(pattern_uni,[status(thm)],[970:[bind(A,$thf( L )),bind(B,$thf( M )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( M @ ( L @ implies ) @ ( M @ ( K @ ( falsehood @ implies ) @ implies ) @ implies ) ))]]) ).
thf(1013,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= c ),
inference(simp,[status(thm)],[971]) ).
thf(273,plain,
! [A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14,264]) ).
thf(274,plain,
! [A: $i] :
( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[273]) ).
thf(284,plain,
! [A: $i] :
( ( A @ ( falsehood @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[274]) ).
thf(12323,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,11895]) ).
thf(12324,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[12323]) ).
thf(12392,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) )
!= ( falsehood @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[12324]) ).
thf(200,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( D @ ( C @ implies ) @ is_a_theorem )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[66,66]) ).
thf(201,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( D @ ( C @ implies ) @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[200]) ).
thf(202,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
| ~ ( C @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[201:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( F @ ( E @ implies ) ))]]) ).
thf(210,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[202]) ).
thf(9165,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ ( C @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9036,210]) ).
thf(9166,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ ( C @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[9165]) ).
thf(9167,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( C @ ( C @ ( D @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[9166:[bind(A,$thf( G )),bind(B,$thf( K )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( G @ ( G @ ( K @ ( falsehood @ implies ) @ implies ) @ implies ) ))]]) ).
thf(9199,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( C @ ( C @ ( D @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[9167]) ).
thf(555,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ ( E @ implies ) @ is_a_theorem ) )
| ( F @ ( E @ implies ) @ ( F @ ( D @ implies ) @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[208,61]) ).
thf(556,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ ( E @ implies ) @ is_a_theorem ) )
| ( F @ ( E @ implies ) @ ( F @ ( D @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[555]) ).
thf(557,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( A @ implies ) @ ( B @ ( D @ ( C @ implies ) @ ( D @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[556:[bind(A,$thf( A )),bind(B,$thf( I )),bind(C,$thf( J )),bind(D,$thf( J @ ( I @ implies ) @ ( J @ implies ) )),bind(E,$thf( A )),bind(F,$thf( F ))]]) ).
thf(618,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( A @ implies ) @ ( B @ ( D @ ( C @ implies ) @ ( D @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[557]) ).
thf(4346,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( D @ ( C @ implies ) @ ( D @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[618,87]) ).
thf(4347,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( D @ ( C @ implies ) @ ( D @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) ),
inference(simp,[status(thm)],[4346]) ).
thf(4368,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( D @ ( C @ implies ) @ ( D @ implies ) @ implies ) @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[4347]) ).
thf(2997,plain,
( ( ( c @ ( b @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( c @ ( b @ implies ) @ ( a @ implies ) )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ( ( c @ ( b @ implies ) @ ( a @ implies ) )
!= ( b @ ( a @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[1836]) ).
thf(3000,plain,
( ( ( c @ ( b @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( c @ ( b @ implies ) )
!= b )
| ( a != a ) ),
inference(simp,[status(thm)],[2997]) ).
thf(3014,plain,
( ( ( c @ ( b @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( c @ ( b @ implies ) )
!= b ) ),
inference(simp,[status(thm)],[3000]) ).
thf(1915,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( c @ ( b @ implies ) ) )
| ( ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) )
!= ( C @ ( A @ implies ) ) )
| ( ( C @ ( A @ implies ) )
!= ( c @ ( b @ implies ) ) )
| ( ( C @ ( B @ implies ) )
!= a )
| ( ( B @ ( A @ implies ) )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[117]) ).
thf(1945,plain,
! [C: $i,B: $i,A: $i] :
( ( B != c )
| ( A != b )
| ( ( c @ ( a @ implies ) )
!= C )
| ( ( b @ ( a @ implies ) )
!= A )
| ( C != c )
| ( A != b )
| ( ( C @ ( B @ implies ) )
!= a )
| ( ( B @ ( A @ implies ) )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[1915]) ).
thf(2024,plain,
( ( ( c @ ( a @ implies ) )
!= c )
| ( ( b @ ( a @ implies ) )
!= b )
| ( ( c @ ( c @ implies ) )
!= a )
| ( ( c @ ( b @ implies ) @ ( a @ implies ) )
!= ( c @ ( b @ implies ) ) ) ),
inference(simp,[status(thm)],[1945]) ).
thf(12641,plain,
! [B: $i,A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( c @ ( B @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14,12231]) ).
thf(12642,plain,
! [B: $i,A: $i] :
( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( c @ ( B @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[12641]) ).
thf(12767,plain,
! [B: $i,A: $i] :
( ( A @ ( falsehood @ implies ) )
!= ( c @ ( B @ ( falsehood @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[12642]) ).
thf(1371,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1241,8]) ).
thf(1372,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1371]) ).
thf(1387,plain,
! [A: $i] :
( ( A @ ( A @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[1372]) ).
thf(2089,plain,
! [A: $i] :
( ( A
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) ) )
| ( A
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[1387]) ).
thf(2090,plain,
( ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[2089]) ).
thf(9086,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9036,61]) ).
thf(9087,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[9086]) ).
thf(9088,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[9087:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( G )),bind(D,$thf( G @ ( I @ ( falsehood @ implies ) @ implies ) )),bind(E,$thf( E ))]]) ).
thf(9190,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[9088]) ).
thf(23800,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ ( c @ ( D @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9190,23207]) ).
thf(23801,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ ( c @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[23800]) ).
thf(23802,plain,
! [A: $i] :
~ ( c @ ( b @ ( a @ ( A @ ( falsehood @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[23801:[bind(A,$thf( b )),bind(B,$thf( a )),bind(C,$thf( J )),bind(D,$thf( b @ ( a @ ( J @ ( falsehood @ implies ) @ implies ) @ implies ) ))]]) ).
thf(24137,plain,
! [A: $i] :
~ ( c @ ( b @ ( a @ ( A @ ( falsehood @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[23802]) ).
thf(1597,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1469,193]) ).
thf(1598,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1597]) ).
thf(1632,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[1598]) ).
thf(564,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= falsehood )
| ~ $true
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[61,206]) ).
thf(565,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= falsehood )
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[564]) ).
thf(566,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( A @ implies ) )
!= falsehood )
| ~ ( B @ ( C @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[565:[bind(A,$thf( H )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( K @ ( J @ implies ) @ ( K @ ( H @ implies ) @ implies ) ))]]) ).
thf(623,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( A @ implies ) )
!= falsehood )
| ~ ( B @ ( C @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[566]) ).
thf(98,plain,
! [A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14,87]) ).
thf(99,plain,
! [A: $i] :
( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) ),
inference(simp,[status(thm)],[98]) ).
thf(106,plain,
! [A: $i] :
( ( A @ ( falsehood @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[99]) ).
thf(12319,plain,
! [B: $i,A: $i] :
( ( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3111,11895]) ).
thf(12320,plain,
! [B: $i,A: $i] :
( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[12319]) ).
thf(12436,plain,
! [B: $i,A: $i] :
( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) )
!= ( falsehood @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[12320]) ).
thf(570,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ ( E @ implies ) @ is_a_theorem ) )
| ( F @ ( E @ implies ) @ ( F @ ( D @ implies ) @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[334,61]) ).
thf(571,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ ( E @ implies ) @ is_a_theorem ) )
| ( F @ ( E @ implies ) @ ( F @ ( D @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[570]) ).
thf(572,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( A @ implies ) @ ( B @ ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[571:[bind(A,$thf( A )),bind(B,$thf( G )),bind(C,$thf( J )),bind(D,$thf( J @ ( falsehood @ implies ) @ ( G @ implies ) )),bind(E,$thf( A )),bind(F,$thf( F ))]]) ).
thf(627,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( A @ implies ) @ ( B @ ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[572]) ).
thf(2567,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[627,264]) ).
thf(2568,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[2567]) ).
thf(2598,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[2568]) ).
thf(4783,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= c )
| ( ( B @ ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[2598]) ).
thf(12127,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ ( a @ implies ) @ is_a_theorem ) )
| ~ ( c @ ( D @ implies ) @ is_a_theorem )
| ~ $true
| ~ ( C @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[210,11441]) ).
thf(12128,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ ( a @ implies ) @ is_a_theorem ) )
| ~ ( c @ ( D @ implies ) @ is_a_theorem )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[12127]) ).
thf(12129,plain,
! [B: $i,A: $i] :
( ~ ( c @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[12128:[bind(A,$thf( a )),bind(B,$thf( E )),bind(C,$thf( F )),bind(D,$thf( F @ ( E @ implies ) ))]]) ).
thf(12236,plain,
! [B: $i,A: $i] :
( ~ ( c @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[12129]) ).
thf(383,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[334,66]) ).
thf(384,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[383]) ).
thf(385,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[384:[bind(A,$thf( F )),bind(B,$thf( H )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( K @ ( falsehood @ implies ) @ ( H @ implies ) @ ( F @ implies ) ))]]) ).
thf(401,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[385]) ).
thf(795,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[401,193]) ).
thf(796,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[795]) ).
thf(821,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[796]) ).
thf(15995,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( a @ implies ) @ is_a_theorem ) )
| ~ ( falsehood @ ( C @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,12356]) ).
thf(15996,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( a @ implies ) @ is_a_theorem ) )
| ~ ( falsehood @ ( C @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[15995]) ).
thf(15997,plain,
! [A: $i] :
~ ( falsehood @ ( a @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[15996:[bind(A,$thf( a )),bind(B,$thf( D )),bind(C,$thf( a @ ( D @ implies ) ))]]) ).
thf(16219,plain,
! [A: $i] :
~ ( falsehood @ ( a @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[15997]) ).
thf(16749,plain,
! [B: $i,A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( falsehood @ ( a @ ( B @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14,16219]) ).
thf(16750,plain,
! [B: $i,A: $i] :
( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( falsehood @ ( a @ ( B @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[16749]) ).
thf(16897,plain,
! [B: $i,A: $i] :
( ( A @ ( falsehood @ implies ) )
!= ( falsehood @ ( a @ ( B @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[16750]) ).
thf(186,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( D @ ( C @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13,66]) ).
thf(187,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( D @ ( C @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[186]) ).
thf(188,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[187:[bind(A,$thf( F )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( F @ ( F @ ( J @ ( F @ implies ) @ implies ) @ implies ) ))]]) ).
thf(211,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[188]) ).
thf(234,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ~ $true
| ( D @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[66,58]) ).
thf(235,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[234]) ).
thf(236,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( B @ implies ) @ is_a_theorem ) )
| ( A @ is_a_theorem )
| ~ ( C @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[235:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( F @ ( E @ implies ) ))]]) ).
thf(253,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( B @ implies ) @ is_a_theorem ) )
| ( A @ is_a_theorem )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[236]) ).
thf(54,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ $true
| ~ ( E @ ( D @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[11,10]) ).
thf(55,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ ( E @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[54]) ).
thf(56,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[55:[bind(A,$thf( N )),bind(B,$thf( L )),bind(C,$thf( O )),bind(D,$thf( O @ ( N @ implies ) @ ( O @ ( L @ implies ) @ implies ) @ ( L @ ( N @ implies ) @ implies ) )),bind(E,$thf( E ))]]) ).
thf(63,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[56]) ).
thf(1220,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( G @ ( F @ implies ) @ ( G @ ( E @ implies ) @ implies ) @ ( E @ ( F @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[487,63]) ).
thf(1221,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( G @ ( F @ implies ) @ ( G @ ( E @ implies ) @ implies ) @ ( E @ ( F @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[1220]) ).
thf(1222,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1221:[bind(A,$thf( T )),bind(B,$thf( R )),bind(C,$thf( U @ ( T @ implies ) @ ( U @ ( R @ implies ) @ implies ) )),bind(D,$thf( U @ ( T @ implies ) @ ( U @ ( R @ implies ) @ implies ) @ ( R @ implies ) )),bind(E,$thf( R )),bind(F,$thf( T )),bind(G,$thf( U ))]]) ).
thf(1245,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1222]) ).
thf(2228,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= falsehood )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1245,206]) ).
thf(2229,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[2228]) ).
thf(2230,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(pattern_uni,[status(thm)],[2229:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( D )),bind(E,$thf( M @ ( L @ implies ) @ ( M @ ( J @ implies ) @ implies ) @ ( J @ implies ) ))]]) ).
thf(2291,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[2230]) ).
thf(1356,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1241,279]) ).
thf(1357,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) ),
inference(simp,[status(thm)],[1356]) ).
thf(1383,plain,
! [A: $i] :
( ( A @ ( A @ implies ) )
!= c ),
inference(simp,[status(thm)],[1357]) ).
thf(3288,plain,
! [B: $i,A: $i] :
( ( A
!= ( c @ ( a @ implies ) ) )
| ( ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) )
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[3180]) ).
thf(3289,plain,
! [A: $i] :
( ( falsehood @ ( A @ ( falsehood @ implies ) @ implies ) )
!= ( b @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[3288]) ).
thf(3290,plain,
! [A: $i] :
( ( falsehood != b )
| ( ( A @ ( falsehood @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[3289]) ).
thf(3077,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[614,87]) ).
thf(3078,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) ),
inference(simp,[status(thm)],[3077]) ).
thf(3093,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[3078]) ).
thf(22693,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ ( C @ implies ) @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ ( C @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13,625]) ).
thf(22694,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ ( C @ implies ) @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ ( C @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[22693]) ).
thf(22695,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( A @ implies ) @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[22694:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( G @ ( I @ ( G @ implies ) @ implies ) )),bind(D,$thf( D )),bind(E,$thf( G ))]]) ).
thf(23069,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( A @ implies ) @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[22695]) ).
thf(2250,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1245,279]) ).
thf(2251,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) ),
inference(simp,[status(thm)],[2250]) ).
thf(2281,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ implies ) )
!= c ),
inference(simp,[status(thm)],[2251]) ).
thf(713,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( D @ implies ) )
!= falsehood )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[334,429]) ).
thf(714,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( D @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[713]) ).
thf(715,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( falsehood @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(pattern_uni,[status(thm)],[714:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( L )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( L @ ( falsehood @ implies ) @ ( I @ implies ) @ ( G @ implies ) ))]]) ).
thf(734,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( falsehood @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[715]) ).
thf(591,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( E @ implies ) @ is_a_theorem ) )
| ( F @ ( E @ implies ) @ ( F @ ( D @ implies ) @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,61]) ).
thf(592,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( E @ implies ) @ is_a_theorem ) )
| ( F @ ( E @ implies ) @ ( F @ ( D @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[591]) ).
thf(593,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ implies ) @ implies ) @ ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[592:[bind(A,$thf( M )),bind(B,$thf( K )),bind(C,$thf( N )),bind(D,$thf( N @ ( M @ implies ) @ ( N @ ( K @ implies ) @ implies ) )),bind(E,$thf( K @ ( M @ implies ) )),bind(F,$thf( F ))]]) ).
thf(621,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ implies ) @ implies ) @ ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[593]) ).
thf(18384,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ implies ) @ implies ) @ ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ ( F @ ( F @ ( G @ ( F @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[621,65]) ).
thf(18385,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ implies ) @ implies ) @ ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ ( F @ ( F @ ( G @ ( F @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( E @ is_a_theorem ) ),
inference(simp,[status(thm)],[18384]) ).
thf(18386,plain,
! [B: $i,A: $i] : ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[18385:[bind(A,$thf( S @ ( R @ implies ) )),bind(B,$thf( S @ ( R @ implies ) )),bind(C,$thf( R )),bind(D,$thf( S )),bind(E,$thf( S @ ( R @ implies ) @ ( S @ ( R @ implies ) @ ( R @ implies ) @ implies ) )),bind(F,$thf( S @ ( R @ implies ) )),bind(G,$thf( S ))]]) ).
thf(18578,plain,
! [B: $i,A: $i] : ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[18386]) ).
thf(1609,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1469,66]) ).
thf(1610,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1609]) ).
thf(1611,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1610:[bind(A,$thf( F )),bind(B,$thf( H )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( K @ ( K @ implies ) @ ( H @ implies ) @ ( F @ implies ) ))]]) ).
thf(1638,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1611]) ).
thf(2497,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( F @ ( E @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1638,66]) ).
thf(2498,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( F @ ( E @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[2497]) ).
thf(2499,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( E @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2498:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( K )),bind(D,$thf( N )),bind(E,$thf( E )),bind(F,$thf( N @ ( N @ implies ) @ ( K @ implies ) @ ( I @ implies ) @ ( G @ implies ) ))]]) ).
thf(2523,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( E @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[2499]) ).
thf(111,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) ) )
| ( B
!= ( c @ ( b @ implies ) ) )
| ( A != a ) ),
inference(simp,[status(thm)],[110]) ).
thf(132,plain,
! [A: $i] :
( ( A @ ( a @ implies ) @ ( A @ ( c @ ( b @ implies ) @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[111]) ).
thf(388,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[334,8]) ).
thf(389,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[388]) ).
thf(396,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[389]) ).
thf(9134,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( D @ ( C @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9036,66]) ).
thf(9135,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( D @ ( C @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[9134]) ).
thf(9136,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[9135:[bind(A,$thf( F )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( F @ ( F @ ( J @ ( falsehood @ implies ) @ implies ) @ implies ) ))]]) ).
thf(9211,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[9136]) ).
thf(9274,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9211,193]) ).
thf(9275,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[9274]) ).
thf(9341,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[9275]) ).
thf(416,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= falsehood )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,206]) ).
thf(417,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[416]) ).
thf(418,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(pattern_uni,[status(thm)],[417:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( H @ ( G @ implies ) @ ( H @ implies ) ))]]) ).
thf(428,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[418]) ).
thf(5051,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( D @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) )
!= c )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4911,297]) ).
thf(5052,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( D @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) )
!= c ) ),
inference(simp,[status(thm)],[5051]) ).
thf(5053,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( E @ implies ) @ ( A @ implies ) )
!= c ),
inference(pattern_uni,[status(thm)],[5052:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( M )),bind(D,$thf( N )),bind(E,$thf( E )),bind(F,$thf( N @ ( M @ implies ) @ ( K @ implies ) @ ( I @ implies ) @ ( N @ implies ) ))]]) ).
thf(5137,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( E @ implies ) @ ( A @ implies ) )
!= c ),
inference(simp,[status(thm)],[5053]) ).
thf(9805,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( E @ ( E @ ( F @ ( E @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9190,65]) ).
thf(9806,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( E @ ( E @ ( F @ ( E @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[9805]) ).
thf(9807,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( A @ ( C @ ( A @ implies ) @ implies ) @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[9806:[bind(A,$thf( L )),bind(B,$thf( L @ ( T @ ( L @ implies ) @ implies ) )),bind(C,$thf( P )),bind(D,$thf( L @ ( L @ ( T @ ( L @ implies ) @ implies ) @ ( P @ ( falsehood @ implies ) @ implies ) @ implies ) )),bind(E,$thf( L )),bind(F,$thf( T ))]]) ).
thf(9896,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( A @ ( C @ ( A @ implies ) @ implies ) @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[9807]) ).
thf(379,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[334,264]) ).
thf(380,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[379]) ).
thf(397,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[380]) ).
thf(666,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) )
| ( B @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14,62]) ).
thf(667,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) )
| ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[666]) ).
thf(687,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ implies ) )
!= ( B @ ( C @ ( falsehood @ implies ) @ implies ) ) )
| ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[667]) ).
thf(1576,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ ( E @ implies ) @ is_a_theorem ) )
| ( F @ ( E @ implies ) @ ( F @ ( D @ implies ) @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1469,61]) ).
thf(1577,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ ( E @ implies ) @ is_a_theorem ) )
| ( F @ ( E @ implies ) @ ( F @ ( D @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1576]) ).
thf(1578,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( A @ implies ) @ ( B @ ( D @ ( D @ implies ) @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1577:[bind(A,$thf( A )),bind(B,$thf( G )),bind(C,$thf( J )),bind(D,$thf( J @ ( J @ implies ) @ ( G @ implies ) )),bind(E,$thf( A )),bind(F,$thf( F ))]]) ).
thf(1637,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( A @ implies ) @ ( B @ ( D @ ( D @ implies ) @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1578]) ).
thf(5197,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( D @ ( D @ implies ) @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1637,87]) ).
thf(5198,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( D @ ( D @ implies ) @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) ),
inference(simp,[status(thm)],[5197]) ).
thf(5220,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( D @ ( D @ implies ) @ ( C @ implies ) @ implies ) @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[5198]) ).
thf(11942,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( C @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( C @ ( a @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[9036,11441]) ).
thf(11943,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( C @ implies ) @ is_a_theorem ) )
| ~ ( C @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[11942]) ).
thf(11944,plain,
! [A: $i] :
~ ( c @ ( A @ ( falsehood @ implies ) @ implies ) @ ( a @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[11943:[bind(A,$thf( c )),bind(B,$thf( G )),bind(C,$thf( c @ ( G @ ( falsehood @ implies ) @ implies ) ))]]) ).
thf(12249,plain,
! [A: $i] :
~ ( c @ ( A @ ( falsehood @ implies ) @ implies ) @ ( a @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[11944]) ).
thf(113,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) )
!= ( c @ ( a @ implies ) ) )
| ( ( C @ ( B @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( B
!= ( c @ ( b @ implies ) ) )
| ( A != a ) ),
inference(simp,[status(thm)],[110]) ).
thf(133,plain,
! [A: $i] :
( ( ( A @ ( a @ implies ) )
!= ( c @ ( a @ implies ) ) )
| ( ( A @ ( c @ ( b @ implies ) @ implies ) )
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[113]) ).
thf(3163,plain,
! [B: $i,A: $i] :
( ( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3111,8]) ).
thf(3164,plain,
! [B: $i,A: $i] :
( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[3163]) ).
thf(3184,plain,
! [B: $i,A: $i] :
( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[3164]) ).
thf(23741,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( D @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ ( c @ ( D @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1247,23207]) ).
thf(23742,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( D @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ ( c @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[23741]) ).
thf(23743,plain,
! [B: $i,A: $i] :
~ ( c @ ( b @ ( a @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[23742:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( b @ ( a @ implies ) )),bind(D,$thf( b @ ( a @ implies ) @ ( I @ implies ) @ ( G @ implies ) ))]]) ).
thf(24125,plain,
! [B: $i,A: $i] :
~ ( c @ ( b @ ( a @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[23743]) ).
thf(3138,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= c )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3111,456]) ).
thf(3139,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= c ) ),
inference(simp,[status(thm)],[3138]) ).
thf(3140,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( falsehood @ ( D @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= c ),
inference(pattern_uni,[status(thm)],[3139:[bind(A,$thf( G )),bind(B,$thf( K )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( G @ ( falsehood @ ( K @ ( falsehood @ implies ) @ implies ) @ implies ) ))]]) ).
thf(3186,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( falsehood @ ( D @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= c ),
inference(simp,[status(thm)],[3140]) ).
thf(4023,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( C @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[210,264]) ).
thf(4024,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[4023]) ).
thf(4127,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) ) )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[4024]) ).
thf(9128,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= ( c @ ( a @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9036,4127]) ).
thf(9129,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= ( c @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[9128]) ).
thf(9130,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(pattern_uni,[status(thm)],[9129:[bind(A,$thf( G )),bind(B,$thf( K )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( G @ ( G @ ( K @ ( falsehood @ implies ) @ implies ) @ implies ) ))]]) ).
thf(9209,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[9130]) ).
thf(10725,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( B @ ( C @ implies ) @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14,609]) ).
thf(10726,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( B @ ( C @ implies ) @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[10725]) ).
thf(10727,plain,
! [B: $i,A: $i] :
( ( B @ ( falsehood @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(pattern_uni,[status(thm)],[10726:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( falsehood ))]]) ).
thf(10922,plain,
! [B: $i,A: $i] :
( ( B @ ( falsehood @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[10727]) ).
thf(1740,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c @ ( a @ implies ) )
!= ( C @ ( B @ implies ) ) )
| ( ( C @ ( A @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( C @ ( B @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( B @ ( A @ implies ) )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[112]) ).
thf(1760,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c @ ( a @ implies ) )
!= ( C @ ( B @ implies ) ) )
| ( C != b )
| ( A != a )
| ( ( C @ ( B @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( B
!= ( c @ ( b @ implies ) ) )
| ( A != a ) ),
inference(simp,[status(thm)],[1740]) ).
thf(1868,plain,
( ( ( b @ ( c @ ( b @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) ) )
| ( ( b @ ( c @ ( b @ implies ) @ implies ) )
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[1760]) ).
thf(5079,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( D @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( F @ ( E @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4911,66]) ).
thf(5080,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( D @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( F @ ( E @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[5079]) ).
thf(5081,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( E @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( E @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[5080:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( M )),bind(D,$thf( N )),bind(E,$thf( E )),bind(F,$thf( N @ ( M @ implies ) @ ( K @ implies ) @ ( I @ implies ) @ ( N @ implies ) ))]]) ).
thf(5122,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( E @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( E @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[5081]) ).
thf(25530,plain,
! [A: $i] :
( ( ( c @ ( b @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ~ ( a @ is_a_theorem ) ),
inference(simp,[status(thm)],[25450]) ).
thf(2999,plain,
( ( ( c @ ( b @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( c @ ( b @ implies ) @ ( a @ implies ) )
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[2997]) ).
thf(3294,plain,
( ( ( b @ ( a @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( c @ ( b @ implies ) @ ( a @ implies ) )
!= ( c @ ( b @ implies ) ) )
| ( ( c @ ( b @ implies ) )
!= ( b @ ( a @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[2999]) ).
thf(3303,plain,
( ( ( c @ ( b @ implies ) @ ( a @ implies ) )
!= ( c @ ( b @ implies ) ) )
| ( ( c @ ( b @ implies ) )
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[3294]) ).
thf(12034,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( a @ implies ) @ is_a_theorem ) )
| ~ ( c @ ( C @ implies ) @ is_a_theorem )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[66,11441]) ).
thf(12035,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( a @ implies ) @ is_a_theorem ) )
| ~ ( c @ ( C @ implies ) @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[12034]) ).
thf(12036,plain,
! [A: $i] :
( ~ ( c @ ( A @ implies ) @ is_a_theorem )
| ~ ( A @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[12035:[bind(A,$thf( a )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(12220,plain,
! [A: $i] :
( ~ ( c @ ( A @ implies ) @ is_a_theorem )
| ~ ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[12036]) ).
thf(14691,plain,
! [A: $i] :
( ~ $true
| ( ( c @ ( A @ implies ) @ is_a_theorem )
!= ( A @ is_a_theorem ) )
| ~ ( A @ is_a_theorem ) ),
inference(eqfactor_ordered,[status(thm)],[12220]) ).
thf(14743,plain,
! [A: $i] :
( ( ( c @ ( A @ implies ) )
!= A )
| ~ ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[14691]) ).
thf(15616,plain,
! [B: $i,A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( ( c @ ( B @ implies ) )
!= B )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14,14743]) ).
thf(15617,plain,
! [B: $i,A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( ( c @ ( B @ implies ) )
!= B ) ),
inference(simp,[status(thm)],[15616]) ).
thf(15618,plain,
! [A: $i] :
( ( c @ ( A @ ( falsehood @ implies ) @ implies ) )
!= ( A @ ( falsehood @ implies ) ) ),
inference(pattern_uni,[status(thm)],[15617:[bind(A,$thf( D )),bind(B,$thf( D @ ( falsehood @ implies ) ))]]) ).
thf(15779,plain,
! [A: $i] :
( ( c @ ( A @ ( falsehood @ implies ) @ implies ) )
!= ( A @ ( falsehood @ implies ) ) ),
inference(simp,[status(thm)],[15618]) ).
thf(258,plain,
! [A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14,193]) ).
thf(259,plain,
! [A: $i] :
( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[258]) ).
thf(270,plain,
! [A: $i] :
( ( A @ ( falsehood @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[259]) ).
thf(510,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[208,193]) ).
thf(511,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[510]) ).
thf(529,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[511]) ).
thf(2237,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= c )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1245,297]) ).
thf(2238,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= c ) ),
inference(simp,[status(thm)],[2237]) ).
thf(2239,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= c ),
inference(pattern_uni,[status(thm)],[2238:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( D )),bind(E,$thf( M @ ( L @ implies ) @ ( M @ ( J @ implies ) @ implies ) @ ( J @ implies ) ))]]) ).
thf(2296,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= c ),
inference(simp,[status(thm)],[2239]) ).
thf(12029,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ ( a @ implies ) @ is_a_theorem ) )
| ~ ( c @ ( D @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[208,11441]) ).
thf(12030,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ ( a @ implies ) @ is_a_theorem ) )
| ~ ( c @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[12029]) ).
thf(12031,plain,
! [B: $i,A: $i] :
~ ( c @ ( B @ ( A @ implies ) @ ( B @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[12030:[bind(A,$thf( a )),bind(B,$thf( G )),bind(C,$thf( H )),bind(D,$thf( H @ ( G @ implies ) @ ( H @ implies ) ))]]) ).
thf(12260,plain,
! [B: $i,A: $i] :
~ ( c @ ( B @ ( A @ implies ) @ ( B @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[12031]) ).
thf(801,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( F @ ( E @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[401,66]) ).
thf(802,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( F @ ( E @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[801]) ).
thf(803,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( E @ ( falsehood @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[802:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( K )),bind(D,$thf( N )),bind(E,$thf( E )),bind(F,$thf( N @ ( falsehood @ implies ) @ ( K @ implies ) @ ( I @ implies ) @ ( G @ implies ) ))]]) ).
thf(825,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( E @ ( falsehood @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[803]) ).
thf(2248,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1245,264]) ).
thf(2249,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[2248]) ).
thf(2277,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[2249]) ).
thf(1515,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1247,193]) ).
thf(1516,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1515]) ).
thf(1550,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[1516]) ).
thf(3021,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) ) )
| ( C
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[1550]) ).
thf(3022,plain,
! [B: $i,A: $i] :
( ( b @ ( a @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[3021]) ).
thf(1484,plain,
! [A: $i] :
( ( A
!= ( c @ ( a @ implies ) ) )
| ( A
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[1386]) ).
thf(1485,plain,
( ( c @ ( a @ implies ) )
!= ( b @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[1484]) ).
thf(1486,plain,
( ( c != b )
| ( a != a ) ),
inference(simp,[status(thm)],[1485]) ).
thf(1487,plain,
c != b,
inference(simp,[status(thm)],[1486]) ).
thf(704,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( D @ implies ) )
!= falsehood )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[208,429]) ).
thf(705,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( D @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[704]) ).
thf(706,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ implies ) @ ( E @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(pattern_uni,[status(thm)],[705:[bind(A,$thf( G )),bind(B,$thf( K )),bind(C,$thf( L )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( L @ ( K @ implies ) @ ( L @ implies ) @ ( G @ implies ) ))]]) ).
thf(729,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ implies ) @ ( E @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[706]) ).
thf(23216,plain,
! [B: $i,A: $i] :
( ( ( B @ ( falsehood @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[207,22675]) ).
thf(23217,plain,
! [B: $i,A: $i] :
( ( B @ ( falsehood @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[23216]) ).
thf(23239,plain,
! [B: $i,A: $i] :
( ( B @ ( falsehood @ implies ) @ ( A @ implies ) )
!= ( c @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[23217]) ).
thf(1223,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[487,87]) ).
thf(1224,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) ),
inference(simp,[status(thm)],[1223]) ).
thf(1238,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[1224]) ).
thf(3435,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3101,264]) ).
thf(3436,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[3435]) ).
thf(3471,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ ( C @ implies ) @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[3436]) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13,8]) ).
thf(22,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[21]) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[22]) ).
thf(69,plain,
! [B: $i,A: $i] :
( ( A
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) ) )
| ( ( A @ ( B @ ( A @ implies ) @ implies ) )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[23]) ).
thf(70,plain,
! [A: $i] :
( ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ ( A @ ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ implies ) )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[69]) ).
thf(23733,plain,
! [B: $i,A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( c @ ( B @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( B @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[14,23207]) ).
thf(23734,plain,
! [B: $i,A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( c @ ( B @ implies ) @ is_a_theorem ) )
| ~ ( B @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[23733]) ).
thf(23735,plain,
~ ( falsehood @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[23734:[bind(A,$thf( c )),bind(B,$thf( falsehood ))]]) ).
thf(24245,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ is_a_theorem )
!= ( falsehood @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( C @ ( A @ implies ) @ is_a_theorem )
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[612,23735]) ).
thf(24246,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ is_a_theorem )
!= ( falsehood @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ ( C @ ( A @ implies ) @ is_a_theorem )
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[24245]) ).
thf(24247,plain,
! [A: $i] :
( ~ ( falsehood @ ( A @ implies ) @ is_a_theorem )
| ~ ( A @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[24246:[bind(A,$thf( A )),bind(B,$thf( b @ ( a @ implies ) )),bind(C,$thf( falsehood ))]]) ).
thf(30156,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( D @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ ( falsehood @ ( D @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1247,24247]) ).
thf(30157,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( D @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ ( falsehood @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[30156]) ).
thf(30158,plain,
! [B: $i,A: $i] :
~ ( falsehood @ ( b @ ( a @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[30157:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( b @ ( a @ implies ) )),bind(D,$thf( b @ ( a @ implies ) @ ( I @ implies ) @ ( G @ implies ) ))]]) ).
thf(30567,plain,
! [B: $i,A: $i] :
~ ( falsehood @ ( b @ ( a @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[30158]) ).
thf(668,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( E @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ $true
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[61,62]) ).
thf(669,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( E @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[668]) ).
thf(670,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ is_a_theorem )
| ~ ( falsehood @ ( A @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[669:[bind(A,$thf( falsehood )),bind(B,$thf( F )),bind(C,$thf( G )),bind(D,$thf( G @ ( F @ implies ) )),bind(E,$thf( G ))]]) ).
thf(693,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ is_a_theorem )
| ~ ( falsehood @ ( A @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[670]) ).
thf(313,plain,
! [B: $i,A: $i] :
( ( ( B @ ( falsehood @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[207,279]) ).
thf(314,plain,
! [B: $i,A: $i] :
( ( B @ ( falsehood @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) ),
inference(simp,[status(thm)],[313]) ).
thf(329,plain,
! [B: $i,A: $i] :
( ( B @ ( falsehood @ implies ) @ ( A @ implies ) )
!= c ),
inference(simp,[status(thm)],[314]) ).
thf(13893,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( B @ ( c @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1241,13835]) ).
thf(13894,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( B @ ( c @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[13893]) ).
thf(14015,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( c @ ( B @ ( c @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[13894]) ).
thf(22045,plain,
! [B: $i,A: $i] :
( ( A != c )
| ( A
!= ( B @ ( c @ implies ) ) ) ),
inference(simp,[status(thm)],[14015]) ).
thf(22046,plain,
! [A: $i] :
( ( A @ ( c @ implies ) )
!= c ),
inference(simp,[status(thm)],[22045]) ).
thf(2577,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( F @ ( E @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[627,66]) ).
thf(2578,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( F @ ( E @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[2577]) ).
thf(2579,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( E @ ( D @ implies ) @ ( E @ ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2578:[bind(A,$thf( O )),bind(B,$thf( P )),bind(C,$thf( K )),bind(D,$thf( N )),bind(E,$thf( E )),bind(F,$thf( P @ ( O @ implies ) @ ( P @ ( N @ ( falsehood @ implies ) @ ( K @ implies ) @ implies ) @ implies ) ))]]) ).
thf(2609,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( E @ ( D @ implies ) @ ( E @ ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[2579]) ).
thf(4186,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) )
!= c )
| ( A != a ) ),
inference(simp,[status(thm)],[2277]) ).
thf(4187,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( a @ implies ) @ implies ) )
!= c ),
inference(simp,[status(thm)],[4186]) ).
thf(441,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= c )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[334,297]) ).
thf(442,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= c ) ),
inference(simp,[status(thm)],[441]) ).
thf(443,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= c ),
inference(pattern_uni,[status(thm)],[442:[bind(A,$thf( F )),bind(B,$thf( H )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( K @ ( falsehood @ implies ) @ ( H @ implies ) @ ( F @ implies ) ))]]) ).
thf(461,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= c ),
inference(simp,[status(thm)],[443]) ).
thf(18314,plain,
! [A: $i] :
( ( c != A )
| ( ( A @ ( falsehood @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[15779]) ).
thf(18315,plain,
( ( c @ ( falsehood @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[18314]) ).
thf(271,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13,264]) ).
thf(272,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[271]) ).
thf(285,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[272]) ).
thf(216,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ~ $true
| ( D @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[13,58]) ).
thf(217,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[216]) ).
thf(218,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( A @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[217:[bind(A,$thf( F )),bind(B,$thf( J )),bind(C,$thf( F @ ( F @ ( J @ ( F @ implies ) @ implies ) @ implies ) )),bind(D,$thf( D ))]]) ).
thf(252,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[218]) ).
thf(1812,plain,
! [C: $i,B: $i,A: $i] :
( ( b != B )
| ( a != A )
| ( ( C @ ( B @ implies ) )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ( C != c )
| ( A != a )
| ( B
!= ( c @ ( b @ implies ) ) )
| ( A != a ) ),
inference(simp,[status(thm)],[1736]) ).
thf(1837,plain,
( ( ( c @ ( b @ implies ) )
!= b )
| ( ( c @ ( c @ ( b @ implies ) @ implies ) )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[1812]) ).
thf(3231,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( falsehood @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3194,193]) ).
thf(3232,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( falsehood @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[3231]) ).
thf(3269,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( falsehood @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[3232]) ).
thf(347,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= C )
| ~ $true
| ( D @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[66,59]) ).
thf(348,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= C )
| ( D @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[347]) ).
thf(349,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ implies ) @ implies ) )
!= ( C @ ( B @ implies ) ) )
| ( A @ is_a_theorem )
| ~ ( C @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[348:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( F @ ( E @ implies ) ))]]) ).
thf(361,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ implies ) @ implies ) )
!= ( C @ ( B @ implies ) ) )
| ( A @ is_a_theorem )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[349]) ).
thf(5091,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( D @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4911,87]) ).
thf(5092,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( D @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) ),
inference(simp,[status(thm)],[5091]) ).
thf(5113,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( D @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[5092]) ).
thf(1354,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1241,264]) ).
thf(1355,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1354]) ).
thf(1384,plain,
! [A: $i] :
( ( A @ ( A @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[1355]) ).
thf(1401,plain,
! [A: $i] :
( ( A != c )
| ( A != a ) ),
inference(simp,[status(thm)],[1384]) ).
thf(1402,plain,
c != a,
inference(simp,[status(thm)],[1401]) ).
thf(9098,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= c )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9036,297]) ).
thf(9099,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= c ) ),
inference(simp,[status(thm)],[9098]) ).
thf(9100,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= c ),
inference(pattern_uni,[status(thm)],[9099:[bind(A,$thf( F )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( F @ ( F @ ( J @ ( falsehood @ implies ) @ implies ) @ implies ) ))]]) ).
thf(9196,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= c ),
inference(simp,[status(thm)],[9100]) ).
thf(856,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= c )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[66,456]) ).
thf(857,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= c )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[856]) ).
thf(858,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= c )
| ~ ( D @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[857:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( G @ ( F @ implies ) ))]]) ).
thf(874,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= c )
| ~ ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[858]) ).
thf(5256,plain,
! [A: $i] :
( ( ( c @ ( a @ implies ) )
!= ( a @ ( A @ implies ) ) )
| ( ( c @ ( b @ implies ) )
!= b )
| ( A != a )
| ( ( a @ ( A @ implies ) )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[5247]) ).
thf(5270,plain,
( ( ( c @ ( a @ implies ) )
!= ( a @ ( a @ implies ) ) )
| ( ( c @ ( b @ implies ) )
!= b )
| ( ( c @ ( b @ implies ) @ ( a @ implies ) )
!= ( a @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[5256]) ).
thf(2342,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( C @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1468,87]) ).
thf(2343,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( C @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) ),
inference(simp,[status(thm)],[2342]) ).
thf(2359,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( C @ ( C @ implies ) @ implies ) @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[2343]) ).
thf(350,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= D )
| ~ $true
| ( E @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[11,59]) ).
thf(351,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= D )
| ( E @ is_a_theorem ) ),
inference(simp,[status(thm)],[350]) ).
thf(352,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ implies ) )
!= ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) ) )
| ( A @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[351:[bind(A,$thf( N )),bind(B,$thf( L )),bind(C,$thf( O )),bind(D,$thf( O @ ( N @ implies ) @ ( O @ ( L @ implies ) @ implies ) @ ( L @ ( N @ implies ) @ implies ) )),bind(E,$thf( E ))]]) ).
thf(356,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ implies ) )
!= ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) ) )
| ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[352]) ).
thf(371,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ $true
| ~ ( E @ ( D @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[334,10]) ).
thf(372,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ ( E @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[371]) ).
thf(373,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[372:[bind(A,$thf( F )),bind(B,$thf( H )),bind(C,$thf( K )),bind(D,$thf( K @ ( falsehood @ implies ) @ ( H @ implies ) @ ( F @ implies ) )),bind(E,$thf( E ))]]) ).
thf(403,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[373]) ).
thf(10135,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( A @ implies ) @ implies ) @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9896,279]) ).
thf(10136,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( A @ implies ) @ implies ) @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) ),
inference(simp,[status(thm)],[10135]) ).
thf(10203,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( A @ implies ) @ implies ) @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) )
!= c ),
inference(simp,[status(thm)],[10136]) ).
thf(4875,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ implies ) @ ( A @ ( D @ ( C @ implies ) @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1561,87]) ).
thf(4876,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ implies ) @ ( A @ ( D @ ( C @ implies ) @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) ),
inference(simp,[status(thm)],[4875]) ).
thf(4898,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ implies ) @ ( A @ ( D @ ( C @ implies ) @ ( B @ implies ) @ implies ) @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[4876]) ).
thf(13346,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ ( B @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1241,12258]) ).
thf(13347,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ ( B @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[13346]) ).
thf(13434,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( c @ ( a @ ( B @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[13347]) ).
thf(3148,plain,
! [B: $i,A: $i] :
( ( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3111,279]) ).
thf(3149,plain,
! [B: $i,A: $i] :
( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) ),
inference(simp,[status(thm)],[3148]) ).
thf(3179,plain,
! [B: $i,A: $i] :
( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) )
!= c ),
inference(simp,[status(thm)],[3149]) ).
thf(23502,plain,
! [A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( c @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14,23340]) ).
thf(23503,plain,
! [A: $i] :
( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( c @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[23502]) ).
thf(23625,plain,
! [A: $i] :
( ( A @ ( falsehood @ implies ) )
!= ( c @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[23503]) ).
thf(15875,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( D @ ( a @ implies ) @ is_a_theorem ) )
| ~ ( falsehood @ ( D @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1247,12356]) ).
thf(15876,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( D @ ( a @ implies ) @ is_a_theorem ) )
| ~ ( falsehood @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[15875]) ).
thf(15877,plain,
! [B: $i,A: $i] :
~ ( falsehood @ ( a @ ( B @ implies ) @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[15876:[bind(A,$thf( E )),bind(B,$thf( G )),bind(C,$thf( a )),bind(D,$thf( a @ ( G @ implies ) @ ( E @ implies ) ))]]) ).
thf(16201,plain,
! [B: $i,A: $i] :
~ ( falsehood @ ( a @ ( B @ implies ) @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[15877]) ).
thf(661,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( D @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) )
| ( C @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13,62]) ).
thf(662,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( D @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) )
| ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[661]) ).
thf(686,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) )
!= ( C @ ( D @ ( falsehood @ implies ) @ implies ) ) )
| ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[662]) ).
thf(23550,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1241,23340]) ).
thf(23551,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[23550]) ).
thf(23635,plain,
! [A: $i] :
( ( A @ ( A @ implies ) )
!= ( c @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[23551]) ).
thf(203,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,66]) ).
thf(204,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[203]) ).
thf(205,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[204:[bind(A,$thf( N )),bind(B,$thf( L )),bind(C,$thf( O )),bind(D,$thf( D )),bind(E,$thf( O @ ( N @ implies ) @ ( O @ ( L @ implies ) @ implies ) @ ( L @ ( N @ implies ) @ implies ) ))]]) ).
thf(212,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[205]) ).
thf(104,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,87]) ).
thf(105,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) ),
inference(simp,[status(thm)],[104]) ).
thf(109,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[105]) ).
thf(309,plain,
! [B: $i,A: $i] :
( ( ( B @ ( falsehood @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[207,193]) ).
thf(310,plain,
! [B: $i,A: $i] :
( ( B @ ( falsehood @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[309]) ).
thf(328,plain,
! [B: $i,A: $i] :
( ( B @ ( falsehood @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[310]) ).
thf(3414,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= falsehood )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3101,206]) ).
thf(3415,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[3414]) ).
thf(3416,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( B @ ( D @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(pattern_uni,[status(thm)],[3415:[bind(A,$thf( K )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( D )),bind(E,$thf( M @ ( L @ implies ) @ ( M @ ( K @ ( M @ implies ) @ implies ) @ implies ) ))]]) ).
thf(3486,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( B @ ( D @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[3416]) ).
thf(2487,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1638,264]) ).
thf(2488,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[2487]) ).
thf(2519,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[2488]) ).
thf(28614,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( falsehood @ ( A @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[693,22877]) ).
thf(28615,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ ( falsehood @ ( A @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[28614]) ).
thf(28616,plain,
~ ( falsehood @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[28615:[bind(A,$thf( c @ ( b @ implies ) @ ( a @ implies ) )),bind(B,$thf( c @ ( a @ implies ) ))]]) ).
thf(29085,plain,
! [A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( falsehood @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14,28616]) ).
thf(29086,plain,
! [A: $i] :
( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( falsehood @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[29085]) ).
thf(29220,plain,
! [A: $i] :
( ( A @ ( falsehood @ implies ) )
!= ( falsehood @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[29086]) ).
thf(450,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= c )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,297]) ).
thf(451,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= c ) ),
inference(simp,[status(thm)],[450]) ).
thf(452,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ ( A @ implies ) )
!= c ),
inference(pattern_uni,[status(thm)],[451:[bind(A,$thf( N )),bind(B,$thf( L )),bind(C,$thf( O )),bind(D,$thf( D )),bind(E,$thf( O @ ( N @ implies ) @ ( O @ ( L @ implies ) @ implies ) @ ( L @ ( N @ implies ) @ implies ) ))]]) ).
thf(457,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ ( A @ implies ) )
!= c ),
inference(simp,[status(thm)],[452]) ).
thf(16933,plain,
! [B: $i,A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( falsehood @ ( B @ ( B @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14,16236]) ).
thf(16934,plain,
! [B: $i,A: $i] :
( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( falsehood @ ( B @ ( B @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[16933]) ).
thf(17096,plain,
! [B: $i,A: $i] :
( ( A @ ( falsehood @ implies ) )
!= ( falsehood @ ( B @ ( B @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[16934]) ).
thf(24256,plain,
! [B: $i,A: $i] :
( ( ( B @ ( falsehood @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[207,23735]) ).
thf(24257,plain,
! [B: $i,A: $i] :
( ( B @ ( falsehood @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[24256]) ).
thf(24313,plain,
! [B: $i,A: $i] :
( ( B @ ( falsehood @ implies ) @ ( A @ implies ) )
!= ( falsehood @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[24257]) ).
thf(561,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( E @ implies ) @ is_a_theorem ) )
| ( F @ ( E @ implies ) @ ( F @ ( D @ implies ) @ implies ) @ is_a_theorem )
| ~ $true
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[61,61]) ).
thf(562,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( E @ implies ) @ is_a_theorem ) )
| ( F @ ( E @ implies ) @ ( F @ ( D @ implies ) @ implies ) @ is_a_theorem )
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[561]) ).
thf(563,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( B @ implies ) @ implies ) @ ( A @ ( D @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
| ~ ( B @ ( C @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[562:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( J )),bind(D,$thf( J @ ( I @ implies ) )),bind(E,$thf( J @ ( G @ implies ) )),bind(F,$thf( F ))]]) ).
thf(622,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( B @ implies ) @ implies ) @ ( A @ ( D @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
| ~ ( B @ ( C @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[563]) ).
thf(792,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) )
!= c )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[401,297]) ).
thf(793,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) )
!= c ) ),
inference(simp,[status(thm)],[792]) ).
thf(794,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( falsehood @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= c ),
inference(pattern_uni,[status(thm)],[793:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( K )),bind(D,$thf( N )),bind(E,$thf( E )),bind(F,$thf( N @ ( falsehood @ implies ) @ ( K @ implies ) @ ( I @ implies ) @ ( G @ implies ) ))]]) ).
thf(837,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( falsehood @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= c ),
inference(simp,[status(thm)],[794]) ).
thf(23706,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ ( c @ ( D @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[614,23207]) ).
thf(23707,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ ( c @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[23706]) ).
thf(23708,plain,
! [A: $i] :
~ ( c @ ( b @ ( a @ ( A @ ( a @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[23707:[bind(A,$thf( b )),bind(B,$thf( a )),bind(C,$thf( J )),bind(D,$thf( b @ ( a @ ( J @ ( a @ implies ) @ implies ) @ implies ) ))]]) ).
thf(24112,plain,
! [A: $i] :
~ ( c @ ( b @ ( a @ ( A @ ( a @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[23708]) ).
thf(8936,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ ( D @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ ( G @ ( F @ implies ) @ ( G @ implies ) @ implies ) @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1021,60]) ).
thf(8937,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ ( D @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ ( G @ ( F @ implies ) @ ( G @ implies ) @ implies ) @ is_a_theorem ) )
| ( E @ is_a_theorem ) ),
inference(simp,[status(thm)],[8936]) ).
thf(8938,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ implies ) @ ( B @ implies ) @ ( D @ ( A @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[8937:[bind(A,$thf( W @ ( V @ implies ) @ ( T @ implies ) )),bind(B,$thf( S )),bind(C,$thf( V )),bind(D,$thf( W )),bind(E,$thf( W @ ( V @ implies ) @ ( T @ implies ) @ ( W @ ( S @ ( falsehood @ implies ) @ implies ) @ implies ) )),bind(F,$thf( T )),bind(G,$thf( W @ ( V @ implies ) ))]]) ).
thf(9053,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ implies ) @ ( B @ implies ) @ ( D @ ( A @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[8938]) ).
thf(4872,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ implies ) @ ( A @ ( D @ ( C @ implies ) @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ ( H @ ( G @ implies ) @ ( H @ ( F @ implies ) @ implies ) @ ( F @ ( G @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1561,63]) ).
thf(4873,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ implies ) @ ( A @ ( D @ ( C @ implies ) @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ ( H @ ( G @ implies ) @ ( H @ ( F @ implies ) @ implies ) @ ( F @ ( G @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( E @ is_a_theorem ) ),
inference(simp,[status(thm)],[4872]) ).
thf(4874,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ implies ) @ ( D @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ ( B @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[4873:[bind(A,$thf( ZB @ ( ZA @ implies ) @ ( ZB @ ( Z @ ( Y @ implies ) @ implies ) @ implies ) )),bind(B,$thf( ZA )),bind(C,$thf( Y )),bind(D,$thf( Z )),bind(E,$thf( ZB @ ( ZA @ implies ) @ ( ZB @ ( Z @ ( Y @ implies ) @ implies ) @ implies ) @ ( Z @ implies ) )),bind(F,$thf( Z @ ( Y @ implies ) )),bind(G,$thf( ZA )),bind(H,$thf( ZB ))]]) ).
thf(4902,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ implies ) @ ( D @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ ( B @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[4874]) ).
thf(1190,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= falsehood )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[487,206]) ).
thf(1191,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[1190]) ).
thf(1192,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(pattern_uni,[status(thm)],[1191:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( D )),bind(E,$thf( M @ ( L @ implies ) @ ( M @ ( L @ ( J @ implies ) @ implies ) @ implies ) ))]]) ).
thf(1246,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[1192]) ).
thf(11945,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ ( a @ implies ) @ is_a_theorem ) )
| ~ ( c @ ( D @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[334,11441]) ).
thf(11946,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ ( a @ implies ) @ is_a_theorem ) )
| ~ ( c @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[11945]) ).
thf(11947,plain,
! [B: $i,A: $i] :
~ ( c @ ( B @ ( falsehood @ implies ) @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[11946:[bind(A,$thf( a )),bind(B,$thf( E )),bind(C,$thf( H )),bind(D,$thf( H @ ( falsehood @ implies ) @ ( E @ implies ) ))]]) ).
thf(12250,plain,
! [B: $i,A: $i] :
~ ( c @ ( B @ ( falsehood @ implies ) @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[11947]) ).
thf(344,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= C )
| ~ $true
| ( D @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[12,59]) ).
thf(345,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= C )
| ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[344]) ).
thf(346,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ implies ) @ ( C @ implies ) @ implies ) )
!= ( C @ ( B @ implies ) @ ( C @ implies ) ) )
| ( A @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[345:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( H @ ( G @ implies ) @ ( H @ implies ) )),bind(D,$thf( D ))]]) ).
thf(360,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ implies ) @ ( C @ implies ) @ implies ) )
!= ( C @ ( B @ implies ) @ ( C @ implies ) ) )
| ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[346]) ).
thf(16008,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ ( a @ implies ) @ is_a_theorem ) )
| ~ ( falsehood @ ( D @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[208,12356]) ).
thf(16009,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ ( a @ implies ) @ is_a_theorem ) )
| ~ ( falsehood @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[16008]) ).
thf(16010,plain,
! [B: $i,A: $i] :
~ ( falsehood @ ( B @ ( A @ implies ) @ ( B @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[16009:[bind(A,$thf( a )),bind(B,$thf( G )),bind(C,$thf( H )),bind(D,$thf( H @ ( G @ implies ) @ ( H @ implies ) ))]]) ).
thf(16220,plain,
! [B: $i,A: $i] :
~ ( falsehood @ ( B @ ( A @ implies ) @ ( B @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[16010]) ).
thf(1497,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= falsehood )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1247,206]) ).
thf(1498,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[1497]) ).
thf(1499,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( D @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(pattern_uni,[status(thm)],[1498:[bind(A,$thf( H )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( K @ ( J @ implies ) @ ( H @ implies ) @ ( K @ implies ) ))]]) ).
thf(1563,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( D @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[1499]) ).
thf(6726,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) )
!= c )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3111,608]) ).
thf(6727,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) )
!= c ) ),
inference(simp,[status(thm)],[6726]) ).
thf(6728,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( falsehood @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= c ),
inference(pattern_uni,[status(thm)],[6727:[bind(A,$thf( A )),bind(B,$thf( I )),bind(C,$thf( A )),bind(D,$thf( falsehood @ ( I @ ( falsehood @ implies ) @ implies ) )),bind(E,$thf( E ))]]) ).
thf(6812,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( falsehood @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= c ),
inference(simp,[status(thm)],[6728]) ).
thf(1137,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[211,66]) ).
thf(1138,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1137]) ).
thf(1139,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( C @ ( C @ ( D @ ( C @ implies ) @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1138:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( M )),bind(D,$thf( D )),bind(E,$thf( I @ ( I @ ( M @ ( I @ implies ) @ implies ) @ implies ) @ ( F @ implies ) ))]]) ).
thf(1170,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( C @ ( C @ ( D @ ( C @ implies ) @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1139]) ).
thf(9137,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) )
!= c )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9036,608]) ).
thf(9138,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) )
!= c ) ),
inference(simp,[status(thm)],[9137]) ).
thf(9139,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) )
!= c ),
inference(pattern_uni,[status(thm)],[9138:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( G )),bind(D,$thf( G @ ( I @ ( falsehood @ implies ) @ implies ) )),bind(E,$thf( E ))]]) ).
thf(9213,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) )
!= c ),
inference(simp,[status(thm)],[9139]) ).
thf(14030,plain,
! [B: $i,A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14,12257]) ).
thf(14031,plain,
! [B: $i,A: $i] :
( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[14030]) ).
thf(14185,plain,
! [B: $i,A: $i] :
( ( A @ ( falsehood @ implies ) )
!= ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[14031]) ).
thf(521,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[208,8]) ).
thf(522,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[521]) ).
thf(530,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[522]) ).
thf(30121,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ ( falsehood @ ( D @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[614,24247]) ).
thf(30122,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ ( falsehood @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[30121]) ).
thf(30123,plain,
! [A: $i] :
~ ( falsehood @ ( b @ ( a @ ( A @ ( a @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[30122:[bind(A,$thf( b )),bind(B,$thf( a )),bind(C,$thf( J )),bind(D,$thf( b @ ( a @ ( J @ ( a @ implies ) @ implies ) @ implies ) ))]]) ).
thf(30555,plain,
! [A: $i] :
~ ( falsehood @ ( b @ ( a @ ( A @ ( a @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[30123]) ).
thf(2326,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( C @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1468,264]) ).
thf(2327,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( C @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[2326]) ).
thf(2357,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( C @ ( C @ implies ) @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[2327]) ).
thf(4288,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= c )
| ( ( B @ ( C @ ( C @ implies ) @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[2357]) ).
thf(381,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[334,279]) ).
thf(382,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) ),
inference(simp,[status(thm)],[381]) ).
thf(398,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= c ),
inference(simp,[status(thm)],[382]) ).
thf(2316,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( C @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= c )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1468,297]) ).
thf(2317,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( C @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= c ) ),
inference(simp,[status(thm)],[2316]) ).
thf(2318,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( B @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= c ),
inference(pattern_uni,[status(thm)],[2317:[bind(A,$thf( L )),bind(B,$thf( M )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( M @ ( L @ implies ) @ ( M @ ( K @ ( K @ implies ) @ implies ) @ implies ) ))]]) ).
thf(2368,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( B @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= c ),
inference(simp,[status(thm)],[2318]) ).
thf(290,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,279]) ).
thf(291,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) ),
inference(simp,[status(thm)],[290]) ).
thf(298,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) )
!= c ),
inference(simp,[status(thm)],[291]) ).
thf(1594,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( D @ implies ) )
!= c )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1469,456]) ).
thf(1595,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( D @ implies ) )
!= c ) ),
inference(simp,[status(thm)],[1594]) ).
thf(1596,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= c ),
inference(pattern_uni,[status(thm)],[1595:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( L )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( L @ ( L @ implies ) @ ( I @ implies ) @ ( G @ implies ) ))]]) ).
thf(1648,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= c ),
inference(simp,[status(thm)],[1596]) ).
thf(422,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= falsehood )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,206]) ).
thf(423,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[422]) ).
thf(424,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(pattern_uni,[status(thm)],[423:[bind(A,$thf( N )),bind(B,$thf( L )),bind(C,$thf( O )),bind(D,$thf( D )),bind(E,$thf( O @ ( N @ implies ) @ ( O @ ( L @ implies ) @ implies ) @ ( L @ ( N @ implies ) @ implies ) ))]]) ).
thf(430,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[424]) ).
thf(15,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,8]) ).
thf(16,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[15]) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[16]) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) ) )
| ( A
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[19]) ).
thf(30,plain,
! [A: $i] :
( ( c @ ( b @ implies ) @ ( a @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[29]) ).
thf(31,plain,
! [A: $i] :
( ( ( c @ ( b @ implies ) @ ( a @ implies ) )
!= ( c @ ( a @ implies ) ) )
| ( A
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[30]) ).
thf(32,plain,
( ( c @ ( b @ implies ) @ ( a @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[31]) ).
thf(710,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( D @ implies ) )
!= falsehood )
| ~ $true
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[61,429]) ).
thf(711,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( D @ implies ) )
!= falsehood )
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[710]) ).
thf(712,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood )
| ~ ( C @ ( D @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[711:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( L )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( L @ ( K @ implies ) @ ( L @ ( I @ implies ) @ implies ) ))]]) ).
thf(733,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood )
| ~ ( C @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[712]) ).
thf(1199,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= c )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[487,297]) ).
thf(1200,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= c ) ),
inference(simp,[status(thm)],[1199]) ).
thf(1201,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= c ),
inference(pattern_uni,[status(thm)],[1200:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( D )),bind(E,$thf( M @ ( L @ implies ) @ ( M @ ( L @ ( J @ implies ) @ implies ) @ implies ) ))]]) ).
thf(1251,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= c ),
inference(simp,[status(thm)],[1201]) ).
thf(30300,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ ( falsehood @ ( C @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,24247]) ).
thf(30301,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ ( falsehood @ ( C @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[30300]) ).
thf(30302,plain,
! [A: $i] :
~ ( falsehood @ ( b @ ( a @ implies ) @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[30301:[bind(A,$thf( b @ ( a @ implies ) )),bind(B,$thf( F )),bind(C,$thf( b @ ( a @ implies ) @ ( F @ implies ) ))]]) ).
thf(30542,plain,
! [A: $i] :
~ ( falsehood @ ( b @ ( a @ implies ) @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[30302]) ).
thf(14446,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( A @ implies ) @ implies ) @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( D @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( D @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[9896,12220]) ).
thf(14447,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( A @ implies ) @ implies ) @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( D @ implies ) @ is_a_theorem ) )
| ~ ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[14446]) ).
thf(14448,plain,
! [B: $i,A: $i] :
~ ( c @ ( B @ ( c @ implies ) @ implies ) @ ( A @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[14447:[bind(A,$thf( c )),bind(B,$thf( H )),bind(C,$thf( L )),bind(D,$thf( c @ ( L @ ( c @ implies ) @ implies ) @ ( H @ ( falsehood @ implies ) @ implies ) ))]]) ).
thf(14777,plain,
! [B: $i,A: $i] :
~ ( c @ ( B @ ( c @ implies ) @ implies ) @ ( A @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[14448]) ).
thf(288,plain,
! [A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14,279]) ).
thf(289,plain,
! [A: $i] :
( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) ),
inference(simp,[status(thm)],[288]) ).
thf(296,plain,
! [A: $i] :
( ( A @ ( falsehood @ implies ) )
!= c ),
inference(simp,[status(thm)],[289]) ).
thf(3207,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( falsehood @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ ( E @ implies ) @ is_a_theorem ) )
| ( F @ ( E @ implies ) @ ( F @ ( D @ implies ) @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3194,61]) ).
thf(3208,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( falsehood @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ ( E @ implies ) @ is_a_theorem ) )
| ( F @ ( E @ implies ) @ ( F @ ( D @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[3207]) ).
thf(3209,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( A @ implies ) @ ( B @ ( C @ ( falsehood @ ( D @ ( falsehood @ implies ) @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[3208:[bind(A,$thf( A )),bind(B,$thf( H )),bind(C,$thf( L )),bind(D,$thf( H @ ( falsehood @ ( L @ ( falsehood @ implies ) @ implies ) @ implies ) )),bind(E,$thf( A )),bind(F,$thf( F ))]]) ).
thf(3274,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( A @ implies ) @ ( B @ ( C @ ( falsehood @ ( D @ ( falsehood @ implies ) @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[3209]) ).
thf(719,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= falsehood )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[66,429]) ).
thf(720,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= falsehood )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[719]) ).
thf(721,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood )
| ~ ( D @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[720:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( G @ ( F @ implies ) ))]]) ).
thf(728,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood )
| ~ ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[721]) ).
thf(3171,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) )
!= falsehood )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3111,728]) ).
thf(3172,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[3171]) ).
thf(3173,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( falsehood @ ( E @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(pattern_uni,[status(thm)],[3172:[bind(A,$thf( H )),bind(B,$thf( L )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( H @ ( falsehood @ ( L @ ( falsehood @ implies ) @ implies ) @ implies ) ))]]) ).
thf(3187,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( falsehood @ ( E @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[3173]) ).
thf(990,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[628,87]) ).
thf(991,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) ),
inference(simp,[status(thm)],[990]) ).
thf(1007,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[991]) ).
thf(1343,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ ( B @ implies ) )
!= c )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1241,297]) ).
thf(1344,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ ( B @ implies ) )
!= c ) ),
inference(simp,[status(thm)],[1343]) ).
thf(1345,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ implies ) )
!= c ),
inference(pattern_uni,[status(thm)],[1344:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( E @ implies ) ))]]) ).
thf(1388,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ implies ) )
!= c ),
inference(simp,[status(thm)],[1345]) ).
thf(13667,plain,
! [B: $i,A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( c @ ( B @ ( c @ implies ) @ implies ) @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14,12254]) ).
thf(13668,plain,
! [B: $i,A: $i] :
( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( c @ ( B @ ( c @ implies ) @ implies ) @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[13667]) ).
thf(13798,plain,
! [B: $i,A: $i] :
( ( A @ ( falsehood @ implies ) )
!= ( c @ ( B @ ( c @ implies ) @ implies ) @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[13668]) ).
thf(5257,plain,
! [A: $i] :
( ( ( c @ ( a @ implies ) )
!= ( a @ ( A @ implies ) ) )
| ( ( c @ ( b @ implies ) )
!= b )
| ( A != a )
| ( ( c @ ( b @ implies ) )
!= a )
| ( A != a ) ),
inference(simp,[status(thm)],[5247]) ).
thf(5271,plain,
( ( ( c @ ( a @ implies ) )
!= ( a @ ( a @ implies ) ) )
| ( ( c @ ( b @ implies ) )
!= b )
| ( ( c @ ( b @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[5257]) ).
thf(3450,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3101,87]) ).
thf(3451,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) ),
inference(simp,[status(thm)],[3450]) ).
thf(3472,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ ( C @ implies ) @ implies ) @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[3451]) ).
thf(841,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( D @ implies ) )
!= c )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[208,456]) ).
thf(842,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( D @ implies ) )
!= c ) ),
inference(simp,[status(thm)],[841]) ).
thf(843,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ implies ) @ ( E @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= c ),
inference(pattern_uni,[status(thm)],[842:[bind(A,$thf( G )),bind(B,$thf( K )),bind(C,$thf( L )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( L @ ( K @ implies ) @ ( L @ implies ) @ ( G @ implies ) ))]]) ).
thf(875,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ implies ) @ ( E @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= c ),
inference(simp,[status(thm)],[843]) ).
thf(15919,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ ( a @ implies ) @ is_a_theorem ) )
| ~ ( falsehood @ ( D @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[334,12356]) ).
thf(15920,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ ( a @ implies ) @ is_a_theorem ) )
| ~ ( falsehood @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[15919]) ).
thf(15921,plain,
! [B: $i,A: $i] :
~ ( falsehood @ ( B @ ( falsehood @ implies ) @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[15920:[bind(A,$thf( a )),bind(B,$thf( E )),bind(C,$thf( H )),bind(D,$thf( H @ ( falsehood @ implies ) @ ( E @ implies ) ))]]) ).
thf(16209,plain,
! [B: $i,A: $i] :
~ ( falsehood @ ( B @ ( falsehood @ implies ) @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[15921]) ).
thf(9131,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) )
!= falsehood )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9036,611]) ).
thf(9132,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[9131]) ).
thf(9133,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) )
!= falsehood ),
inference(pattern_uni,[status(thm)],[9132:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( G )),bind(D,$thf( G @ ( I @ ( falsehood @ implies ) @ implies ) )),bind(E,$thf( E ))]]) ).
thf(9210,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[9133]) ).
thf(17564,plain,
! [B: $i,A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( ( falsehood @ ( B @ implies ) )
!= B )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14,17428]) ).
thf(17565,plain,
! [B: $i,A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( ( falsehood @ ( B @ implies ) )
!= B ) ),
inference(simp,[status(thm)],[17564]) ).
thf(17566,plain,
! [A: $i] :
( ( falsehood @ ( A @ ( falsehood @ implies ) @ implies ) )
!= ( A @ ( falsehood @ implies ) ) ),
inference(pattern_uni,[status(thm)],[17565:[bind(A,$thf( D )),bind(B,$thf( D @ ( falsehood @ implies ) ))]]) ).
thf(17744,plain,
! [A: $i] :
( ( falsehood @ ( A @ ( falsehood @ implies ) @ implies ) )
!= ( A @ ( falsehood @ implies ) ) ),
inference(simp,[status(thm)],[17566]) ).
thf(12371,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1395,11895]) ).
thf(12372,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[12371]) ).
thf(12401,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ implies ) )
!= ( falsehood @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[12372]) ).
thf(7242,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) )
!= falsehood )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,611]) ).
thf(7243,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[7242]) ).
thf(7244,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ implies ) @ ( A @ ( C @ ( B @ implies ) @ implies ) @ implies ) )
!= falsehood ),
inference(pattern_uni,[status(thm)],[7243:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G @ ( F @ implies ) )),bind(D,$thf( G ))]]) ).
thf(7347,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ implies ) @ ( A @ ( C @ ( B @ implies ) @ implies ) @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[7244]) ).
thf(1450,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1395,8]) ).
thf(1451,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1450]) ).
thf(1464,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[1451]) ).
thf(501,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= falsehood )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[208,206]) ).
thf(502,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[501]) ).
thf(503,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(pattern_uni,[status(thm)],[502:[bind(A,$thf( F )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( K @ ( J @ implies ) @ ( K @ implies ) @ ( F @ implies ) ))]]) ).
thf(540,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[503]) ).
thf(71,plain,
! [A: $i] :
( ( ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) )
!= ( c @ ( b @ implies ) ) )
| ( ( A @ ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[70]) ).
thf(11901,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( D @ ( a @ implies ) @ is_a_theorem ) )
| ~ ( c @ ( D @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1247,11441]) ).
thf(11902,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( D @ ( a @ implies ) @ is_a_theorem ) )
| ~ ( c @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[11901]) ).
thf(11903,plain,
! [B: $i,A: $i] :
~ ( c @ ( a @ ( B @ implies ) @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[11902:[bind(A,$thf( E )),bind(B,$thf( G )),bind(C,$thf( a )),bind(D,$thf( a @ ( G @ implies ) @ ( E @ implies ) ))]]) ).
thf(12242,plain,
! [B: $i,A: $i] :
~ ( c @ ( a @ ( B @ implies ) @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[11903]) ).
thf(28592,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( A @ implies ) @ implies ) @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ ( D @ implies ) @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9896,693]) ).
thf(28593,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( A @ implies ) @ implies ) @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ ( D @ implies ) @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[28592]) ).
thf(28594,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( falsehood @ ( C @ ( falsehood @ implies ) @ implies ) @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[28593:[bind(A,$thf( falsehood )),bind(B,$thf( I )),bind(C,$thf( M )),bind(D,$thf( falsehood @ ( M @ ( falsehood @ implies ) @ implies ) @ ( I @ ( falsehood @ implies ) @ implies ) )),bind(E,$thf( E ))]]) ).
thf(29046,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( falsehood @ ( C @ ( falsehood @ implies ) @ implies ) @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[28594]) ).
thf(4671,plain,
! [B: $i,A: $i] :
( ( A
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) ) )
| ( ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[3184]) ).
thf(4672,plain,
! [A: $i] :
( ( falsehood @ ( A @ ( falsehood @ implies ) @ implies ) )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[4671]) ).
thf(10995,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( B @ ( C @ implies ) @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14,610]) ).
thf(10996,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( B @ ( C @ implies ) @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[10995]) ).
thf(10997,plain,
! [B: $i,A: $i] :
( ( B @ ( falsehood @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(pattern_uni,[status(thm)],[10996:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( falsehood ))]]) ).
thf(11201,plain,
! [B: $i,A: $i] :
( ( B @ ( falsehood @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[10997]) ).
thf(9223,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) ) )
| ( A
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[530]) ).
thf(9224,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[9223]) ).
thf(18308,plain,
! [B: $i,A: $i] :
( ( A != c )
| ( ( B @ ( c @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[13975]) ).
thf(18309,plain,
! [A: $i] :
( ( A @ ( c @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[18308]) ).
thf(780,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ ( F @ implies ) @ is_a_theorem ) )
| ( G @ ( F @ implies ) @ ( G @ ( E @ implies ) @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[401,61]) ).
thf(781,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ ( F @ implies ) @ is_a_theorem ) )
| ( G @ ( F @ implies ) @ ( G @ ( E @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[780]) ).
thf(782,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( B @ ( A @ implies ) @ ( B @ ( E @ ( falsehood @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[781:[bind(A,$thf( A )),bind(B,$thf( H )),bind(C,$thf( J )),bind(D,$thf( M )),bind(E,$thf( M @ ( falsehood @ implies ) @ ( J @ implies ) @ ( H @ implies ) )),bind(F,$thf( A )),bind(G,$thf( G ))]]) ).
thf(831,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( B @ ( A @ implies ) @ ( B @ ( E @ ( falsehood @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[782]) ).
thf(30376,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ ( falsehood @ ( D @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,24247]) ).
thf(30377,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ ( falsehood @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[30376]) ).
thf(30378,plain,
! [A: $i] :
~ ( falsehood @ ( A @ ( a @ implies ) @ ( A @ ( b @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[30377:[bind(A,$thf( a )),bind(B,$thf( b )),bind(C,$thf( J )),bind(D,$thf( J @ ( a @ implies ) @ ( J @ ( b @ implies ) @ implies ) ))]]) ).
thf(30554,plain,
! [A: $i] :
~ ( falsehood @ ( A @ ( a @ implies ) @ ( A @ ( b @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[30378]) ).
thf(10166,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( A @ implies ) @ implies ) @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9896,87]) ).
thf(10167,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( A @ implies ) @ implies ) @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) ),
inference(simp,[status(thm)],[10166]) ).
thf(10204,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( A @ implies ) @ implies ) @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[10167]) ).
thf(701,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= falsehood )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13,429]) ).
thf(702,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[701]) ).
thf(703,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ ( C @ implies ) @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(pattern_uni,[status(thm)],[702:[bind(A,$thf( G )),bind(B,$thf( K )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( G @ ( G @ ( K @ ( G @ implies ) @ implies ) @ implies ) ))]]) ).
thf(736,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ ( C @ implies ) @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[703]) ).
thf(9692,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( D @ ( A @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9053,87]) ).
thf(9693,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( D @ ( A @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) ),
inference(simp,[status(thm)],[9692]) ).
thf(9723,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( D @ ( A @ ( falsehood @ implies ) @ implies ) @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[9693]) ).
thf(552,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= D )
| ~ $true
| ( E @ is_a_theorem )
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[61,59]) ).
thf(553,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= D )
| ( E @ is_a_theorem )
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[552]) ).
thf(554,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ implies ) )
!= ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) ) )
| ( A @ is_a_theorem )
| ~ ( B @ ( C @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[553:[bind(A,$thf( H )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( K @ ( J @ implies ) @ ( K @ ( H @ implies ) @ implies ) )),bind(E,$thf( E ))]]) ).
thf(616,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ implies ) )
!= ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) ) )
| ( A @ is_a_theorem )
| ~ ( B @ ( C @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[554]) ).
thf(9276,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9211,264]) ).
thf(9277,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[9276]) ).
thf(9344,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[9277]) ).
thf(7191,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( B @ ( C @ implies ) @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) )
!= falsehood )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14,611]) ).
thf(7192,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( B @ ( C @ implies ) @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[7191]) ).
thf(7193,plain,
! [B: $i,A: $i] :
( ( B @ ( falsehood @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= falsehood ),
inference(pattern_uni,[status(thm)],[7192:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( falsehood ))]]) ).
thf(7330,plain,
! [B: $i,A: $i] :
( ( B @ ( falsehood @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[7193]) ).
thf(3133,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= c )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3111,297]) ).
thf(3134,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= c ) ),
inference(simp,[status(thm)],[3133]) ).
thf(3135,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( falsehood @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= c ),
inference(pattern_uni,[status(thm)],[3134:[bind(A,$thf( F )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( F @ ( falsehood @ ( J @ ( falsehood @ implies ) @ implies ) @ implies ) ))]]) ).
thf(3197,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( falsehood @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= c ),
inference(simp,[status(thm)],[3135]) ).
thf(413,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= falsehood )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[334,206]) ).
thf(414,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[413]) ).
thf(415,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(pattern_uni,[status(thm)],[414:[bind(A,$thf( F )),bind(B,$thf( H )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( K @ ( falsehood @ implies ) @ ( H @ implies ) @ ( F @ implies ) ))]]) ).
thf(434,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[415]) ).
thf(3146,plain,
! [B: $i,A: $i] :
( ( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3111,264]) ).
thf(3147,plain,
! [B: $i,A: $i] :
( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[3146]) ).
thf(3182,plain,
! [B: $i,A: $i] :
( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[3147]) ).
thf(2838,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( falsehood @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[825,264]) ).
thf(2839,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( falsehood @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[2838]) ).
thf(2871,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( falsehood @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[2839]) ).
thf(1512,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( D @ implies ) )
!= c )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1247,456]) ).
thf(1513,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( D @ implies ) )
!= c ) ),
inference(simp,[status(thm)],[1512]) ).
thf(1514,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ implies ) @ ( C @ implies ) @ ( E @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= c ),
inference(pattern_uni,[status(thm)],[1513:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( L )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( L @ ( K @ implies ) @ ( I @ implies ) @ ( L @ implies ) ))]]) ).
thf(1557,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ implies ) @ ( C @ implies ) @ ( E @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= c ),
inference(simp,[status(thm)],[1514]) ).
thf(463,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( E @ ( D @ implies ) @ ( E @ implies ) @ implies ) @ is_a_theorem ) )
| ( C @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13,60]) ).
thf(464,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( E @ ( D @ implies ) @ ( E @ implies ) @ implies ) @ is_a_theorem ) )
| ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[463]) ).
thf(483,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) )
!= ( C @ ( E @ ( D @ implies ) @ ( E @ implies ) @ implies ) ) )
| ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[464]) ).
thf(12365,plain,
! [B: $i,A: $i] :
( ( ( B @ ( falsehood @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[207,11895]) ).
thf(12366,plain,
! [B: $i,A: $i] :
( ( B @ ( falsehood @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[12365]) ).
thf(12381,plain,
! [B: $i,A: $i] :
( ( B @ ( falsehood @ implies ) @ ( A @ implies ) )
!= ( falsehood @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[12366]) ).
thf(444,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= c )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,297]) ).
thf(445,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= c ) ),
inference(simp,[status(thm)],[444]) ).
thf(446,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) )
!= c ),
inference(pattern_uni,[status(thm)],[445:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( H @ ( G @ implies ) @ ( H @ implies ) ))]]) ).
thf(462,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) )
!= c ),
inference(simp,[status(thm)],[446]) ).
thf(6732,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) )
!= c )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,608]) ).
thf(6733,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) )
!= c ) ),
inference(simp,[status(thm)],[6732]) ).
thf(6734,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ implies ) @ ( A @ ( C @ ( B @ implies ) @ implies ) @ implies ) )
!= c ),
inference(pattern_uni,[status(thm)],[6733:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G @ ( F @ implies ) )),bind(D,$thf( G ))]]) ).
thf(6817,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ implies ) @ ( A @ ( C @ ( B @ implies ) @ implies ) @ implies ) )
!= c ),
inference(simp,[status(thm)],[6734]) ).
thf(102,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,87]) ).
thf(103,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) ),
inference(simp,[status(thm)],[102]) ).
thf(108,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[103]) ).
thf(318,plain,
! [B: $i,A: $i] :
( ( ( B @ ( falsehood @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[207,8]) ).
thf(319,plain,
! [B: $i,A: $i] :
( ( B @ ( falsehood @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[318]) ).
thf(330,plain,
! [B: $i,A: $i] :
( ( B @ ( falsehood @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[319]) ).
thf(11058,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ ( C @ implies ) @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1241,610]) ).
thf(11059,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ ( C @ implies ) @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[11058]) ).
thf(11060,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(pattern_uni,[status(thm)],[11059:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(11173,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[11060]) ).
thf(386,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[334,87]) ).
thf(387,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) ),
inference(simp,[status(thm)],[386]) ).
thf(399,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[387]) ).
thf(5174,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( D @ ( D @ implies ) @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1637,279]) ).
thf(5175,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( D @ ( D @ implies ) @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) ),
inference(simp,[status(thm)],[5174]) ).
thf(5216,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( D @ ( D @ implies ) @ ( C @ implies ) @ implies ) @ implies ) )
!= c ),
inference(simp,[status(thm)],[5175]) ).
thf(1065,plain,
! [B: $i,A: $i] :
( ( A != c )
| ( ( A @ ( B @ ( A @ implies ) @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[285]) ).
thf(1066,plain,
! [A: $i] :
( ( c @ ( A @ ( c @ implies ) @ implies ) )
!= a ),
inference(simp,[status(thm)],[1065]) ).
thf(6795,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ ( E @ implies ) @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( F @ ( D @ implies ) @ implies ) )
!= c )
| ~ $true
| ~ ( C @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[210,608]) ).
thf(6796,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ ( E @ implies ) @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( F @ ( D @ implies ) @ implies ) )
!= c )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[6795]) ).
thf(6797,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( D @ ( C @ implies ) @ implies ) @ implies ) )
!= c )
| ~ ( D @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[6796:[bind(A,$thf( A )),bind(B,$thf( G )),bind(C,$thf( H )),bind(D,$thf( H @ ( G @ implies ) )),bind(E,$thf( A ))]]) ).
thf(6816,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( D @ ( C @ implies ) @ implies ) @ implies ) )
!= c )
| ~ ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[6797]) ).
thf(294,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,279]) ).
thf(295,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) ),
inference(simp,[status(thm)],[294]) ).
thf(299,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= c ),
inference(simp,[status(thm)],[295]) ).
thf(407,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= falsehood )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13,206]) ).
thf(408,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[407]) ).
thf(409,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(pattern_uni,[status(thm)],[408:[bind(A,$thf( F )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( F @ ( F @ ( J @ ( F @ implies ) @ implies ) @ implies ) ))]]) ).
thf(431,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[409]) ).
thf(1334,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ ( B @ implies ) )
!= falsehood )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1241,206]) ).
thf(1335,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ ( B @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[1334]) ).
thf(1336,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(pattern_uni,[status(thm)],[1335:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( E @ implies ) ))]]) ).
thf(1396,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[1336]) ).
thf(2406,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( D @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1562,264]) ).
thf(2407,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( D @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[2406]) ).
thf(2439,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( D @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[2407]) ).
thf(30228,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ ( falsehood @ ( D @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9190,24247]) ).
thf(30229,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ ( falsehood @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[30228]) ).
thf(30230,plain,
! [A: $i] :
~ ( falsehood @ ( b @ ( a @ ( A @ ( falsehood @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[30229:[bind(A,$thf( b )),bind(B,$thf( a )),bind(C,$thf( J )),bind(D,$thf( b @ ( a @ ( J @ ( falsehood @ implies ) @ implies ) @ implies ) ))]]) ).
thf(30532,plain,
! [A: $i] :
~ ( falsehood @ ( b @ ( a @ ( A @ ( falsehood @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[30230]) ).
thf(145,plain,
! [A: $i] :
( ( A != c )
| ( a != a )
| ( ( A @ ( c @ ( b @ implies ) @ implies ) )
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[133]) ).
thf(167,plain,
( ( c @ ( c @ ( b @ implies ) @ implies ) )
!= ( b @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[145]) ).
thf(24202,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1241,23735]) ).
thf(24203,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[24202]) ).
thf(24314,plain,
! [A: $i] :
( ( A @ ( A @ implies ) )
!= ( falsehood @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[24203]) ).
thf(17174,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( A @ implies ) @ implies ) @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ ( D @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( D @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[9896,16221]) ).
thf(17175,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( A @ implies ) @ implies ) @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ ( D @ implies ) @ is_a_theorem ) )
| ~ ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[17174]) ).
thf(17176,plain,
! [B: $i,A: $i] :
~ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ ( A @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[17175:[bind(A,$thf( falsehood )),bind(B,$thf( H )),bind(C,$thf( L )),bind(D,$thf( falsehood @ ( L @ ( falsehood @ implies ) @ implies ) @ ( H @ ( falsehood @ implies ) @ implies ) ))]]) ).
thf(17487,plain,
! [B: $i,A: $i] :
~ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ ( A @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[17176]) ).
thf(585,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem )
| ~ $true
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[61,66]) ).
thf(586,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem )
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[585]) ).
thf(587,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
| ~ ( B @ ( C @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[586:[bind(A,$thf( H )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( K @ ( J @ implies ) @ ( K @ ( H @ implies ) @ implies ) ))]]) ).
thf(617,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
| ~ ( B @ ( C @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[587]) ).
thf(23695,plain,
! [A: $i] :
( ( A != c )
| ( A
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[23635]) ).
thf(23696,plain,
( ( c @ ( b @ implies ) @ ( a @ implies ) )
!= c ),
inference(simp,[status(thm)],[23695]) ).
thf(2569,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[627,279]) ).
thf(2570,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) ),
inference(simp,[status(thm)],[2569]) ).
thf(2597,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ implies ) @ implies ) )
!= c ),
inference(simp,[status(thm)],[2570]) ).
thf(2898,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) )
!= ( c @ ( a @ implies ) ) )
| ( A
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[529]) ).
thf(2899,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[2898]) ).
thf(1503,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( D @ implies ) )
!= falsehood )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1247,429]) ).
thf(1504,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( D @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[1503]) ).
thf(1505,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ implies ) @ ( C @ implies ) @ ( E @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(pattern_uni,[status(thm)],[1504:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( L )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( L @ ( K @ implies ) @ ( I @ implies ) @ ( L @ implies ) ))]]) ).
thf(1551,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ implies ) @ ( C @ implies ) @ ( E @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[1505]) ).
thf(9658,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( D @ ( A @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9053,264]) ).
thf(9659,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( D @ ( A @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[9658]) ).
thf(9727,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( D @ ( A @ ( falsehood @ implies ) @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[9659]) ).
thf(512,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[208,264]) ).
thf(513,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[512]) ).
thf(531,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[513]) ).
thf(183,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ $true
| ~ ( D @ ( C @ implies ) @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[66,10]) ).
thf(184,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ ( D @ ( C @ implies ) @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[183]) ).
thf(185,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( C @ ( B @ implies ) @ implies ) @ is_a_theorem )
| ~ ( C @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[184:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( F @ ( E @ implies ) ))]]) ).
thf(209,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( C @ ( B @ implies ) @ implies ) @ is_a_theorem )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[185]) ).
thf(5042,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( D @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) )
!= falsehood )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4911,206]) ).
thf(5043,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( D @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[5042]) ).
thf(5044,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( E @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(pattern_uni,[status(thm)],[5043:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( M )),bind(D,$thf( N )),bind(E,$thf( E )),bind(F,$thf( N @ ( M @ implies ) @ ( K @ implies ) @ ( I @ implies ) @ ( N @ implies ) ))]]) ).
thf(5133,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( E @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[5044]) ).
thf(435,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= c )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13,297]) ).
thf(436,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= c ) ),
inference(simp,[status(thm)],[435]) ).
thf(437,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= c ),
inference(pattern_uni,[status(thm)],[436:[bind(A,$thf( F )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( F @ ( F @ ( J @ ( F @ implies ) @ implies ) @ implies ) ))]]) ).
thf(458,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= c ),
inference(simp,[status(thm)],[437]) ).
thf(11863,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ ( a @ implies ) @ is_a_theorem ) )
| ~ ( c @ ( D @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1469,11441]) ).
thf(11864,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ ( a @ implies ) @ is_a_theorem ) )
| ~ ( c @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[11863]) ).
thf(11865,plain,
! [B: $i,A: $i] :
~ ( c @ ( B @ ( B @ implies ) @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[11864:[bind(A,$thf( a )),bind(B,$thf( E )),bind(C,$thf( H )),bind(D,$thf( H @ ( H @ implies ) @ ( E @ implies ) ))]]) ).
thf(12234,plain,
! [B: $i,A: $i] :
~ ( c @ ( B @ ( B @ implies ) @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[11865]) ).
thf(797,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[401,264]) ).
thf(798,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[797]) ).
thf(823,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[798]) ).
thf(1731,plain,
! [C: $i,B: $i,A: $i] :
( ( C != c )
| ( A != a )
| ( ( C @ ( B @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( B @ ( A @ implies ) )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[112]) ).
thf(1845,plain,
! [A: $i] :
( ( ( c @ ( A @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( A @ ( a @ implies ) )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[1731]) ).
thf(1532,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1247,87]) ).
thf(1533,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) ),
inference(simp,[status(thm)],[1532]) ).
thf(1547,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[1533]) ).
thf(4326,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( D @ ( C @ implies ) @ ( D @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[618,279]) ).
thf(4327,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( D @ ( C @ implies ) @ ( D @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) ),
inference(simp,[status(thm)],[4326]) ).
thf(4366,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( D @ ( C @ implies ) @ ( D @ implies ) @ implies ) @ implies ) )
!= c ),
inference(simp,[status(thm)],[4327]) ).
thf(4673,plain,
! [A: $i] :
( ( ( c @ ( b @ implies ) )
!= falsehood )
| ( ( A @ ( falsehood @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[4672]) ).
thf(81,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) )
| ( C @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13,35]) ).
thf(82,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) )
| ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[81]) ).
thf(95,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) )
!= falsehood )
| ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[82]) ).
thf(12315,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1241,11895]) ).
thf(12316,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[12315]) ).
thf(12390,plain,
! [A: $i] :
( ( A @ ( A @ implies ) )
!= ( falsehood @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[12316]) ).
thf(311,plain,
! [B: $i,A: $i] :
( ( ( B @ ( falsehood @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[207,264]) ).
thf(312,plain,
! [B: $i,A: $i] :
( ( B @ ( falsehood @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[311]) ).
thf(327,plain,
! [B: $i,A: $i] :
( ( B @ ( falsehood @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[312]) ).
thf(23835,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( C @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( C @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[13,23207]) ).
thf(23836,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( C @ implies ) @ is_a_theorem ) )
| ~ ( C @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[23835]) ).
thf(23837,plain,
! [A: $i] :
~ ( c @ ( A @ ( c @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[23836:[bind(A,$thf( c )),bind(B,$thf( G )),bind(C,$thf( c @ ( G @ ( c @ implies ) @ implies ) ))]]) ).
thf(24093,plain,
! [A: $i] :
~ ( c @ ( A @ ( c @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[23837]) ).
thf(10133,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( A @ implies ) @ implies ) @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9896,264]) ).
thf(10134,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( A @ implies ) @ implies ) @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[10133]) ).
thf(10196,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( A @ implies ) @ implies ) @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[10134]) ).
thf(275,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,264]) ).
thf(276,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[275]) ).
thf(282,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[276]) ).
thf(1130,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[211,264]) ).
thf(1131,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1130]) ).
thf(1156,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[1131]) ).
thf(1265,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= falsehood )
| ~ $true
| ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) )
!= falsehood ) ),
inference(paramod_ordered,[status(thm)],[95,206]) ).
thf(1266,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= falsehood )
| ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[1265]) ).
thf(1267,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( D @ implies ) )
!= falsehood )
| ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) )
!= falsehood ) ),
inference(pattern_uni,[status(thm)],[1266:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( C ))]]) ).
thf(4852,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ implies ) @ ( A @ ( D @ ( C @ implies ) @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1561,279]) ).
thf(4853,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ implies ) @ ( A @ ( D @ ( C @ implies ) @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) ),
inference(simp,[status(thm)],[4852]) ).
thf(4894,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ implies ) @ ( A @ ( D @ ( C @ implies ) @ ( B @ implies ) @ implies ) @ implies ) )
!= c ),
inference(simp,[status(thm)],[4853]) ).
thf(304,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( falsehood @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ $true
| ~ ( D @ ( C @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[207,10]) ).
thf(305,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( falsehood @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ ( D @ ( C @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[304]) ).
thf(306,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[305:[bind(A,$thf( E )),bind(B,$thf( H )),bind(C,$thf( H @ ( falsehood @ implies ) @ ( E @ implies ) )),bind(D,$thf( D ))]]) ).
thf(331,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[306]) ).
thf(3536,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( C @ ( falsehood @ ( D @ ( falsehood @ implies ) @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3274,87]) ).
thf(3537,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( C @ ( falsehood @ ( D @ ( falsehood @ implies ) @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) ),
inference(simp,[status(thm)],[3536]) ).
thf(3554,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( C @ ( falsehood @ ( D @ ( falsehood @ implies ) @ implies ) @ implies ) @ implies ) @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[3537]) ).
thf(2263,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1245,87]) ).
thf(2264,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) ),
inference(simp,[status(thm)],[2263]) ).
thf(2276,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[2264]) ).
thf(15837,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ ( a @ implies ) @ is_a_theorem ) )
| ~ ( falsehood @ ( D @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1469,12356]) ).
thf(15838,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ ( a @ implies ) @ is_a_theorem ) )
| ~ ( falsehood @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[15837]) ).
thf(15839,plain,
! [B: $i,A: $i] :
~ ( falsehood @ ( B @ ( B @ implies ) @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[15838:[bind(A,$thf( a )),bind(B,$thf( E )),bind(C,$thf( H )),bind(D,$thf( H @ ( H @ implies ) @ ( E @ implies ) ))]]) ).
thf(16234,plain,
! [B: $i,A: $i] :
~ ( falsehood @ ( B @ ( B @ implies ) @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[15839]) ).
thf(18306,plain,
! [B: $i,A: $i] :
( ( A != c )
| ( ( a @ ( B @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[13462]) ).
thf(18307,plain,
! [A: $i] :
( ( a @ ( A @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[18306]) ).
thf(341,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( ( C @ ( B @ implies ) )
!= B )
| ~ $true
| ( C @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[14,59]) ).
thf(342,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( ( C @ ( B @ implies ) )
!= B )
| ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[341]) ).
thf(343,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( falsehood @ implies ) @ implies ) )
!= ( B @ ( falsehood @ implies ) ) )
| ( A @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[342:[bind(A,$thf( E )),bind(B,$thf( E @ ( falsehood @ implies ) )),bind(C,$thf( C ))]]) ).
thf(359,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( falsehood @ implies ) @ implies ) )
!= ( B @ ( falsehood @ implies ) ) )
| ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[343]) ).
thf(3064,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[614,279]) ).
thf(3065,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) ),
inference(simp,[status(thm)],[3064]) ).
thf(3095,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) )
!= c ),
inference(simp,[status(thm)],[3065]) ).
thf(6162,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5885,279]) ).
thf(6163,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) ),
inference(simp,[status(thm)],[6162]) ).
thf(6206,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ ( A @ implies ) @ implies ) @ implies ) )
!= c ),
inference(simp,[status(thm)],[6163]) ).
thf(9095,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= falsehood )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9036,429]) ).
thf(9096,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[9095]) ).
thf(9097,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(pattern_uni,[status(thm)],[9096:[bind(A,$thf( G )),bind(B,$thf( K )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( G @ ( G @ ( K @ ( falsehood @ implies ) @ implies ) @ implies ) ))]]) ).
thf(9194,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[9097]) ).
thf(546,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ $true
| ~ ( E @ ( D @ implies ) @ is_a_theorem )
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[61,10]) ).
thf(547,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ ( E @ ( D @ implies ) @ is_a_theorem )
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[546]) ).
thf(548,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
| ~ ( B @ ( C @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[547:[bind(A,$thf( H )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( K @ ( J @ implies ) @ ( K @ ( H @ implies ) @ implies ) )),bind(E,$thf( E ))]]) ).
thf(613,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
| ~ ( B @ ( C @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[548]) ).
thf(3023,plain,
! [B: $i,A: $i] :
( ( ( b @ ( a @ implies ) @ ( B @ implies ) )
!= c )
| ( A != a ) ),
inference(simp,[status(thm)],[3022]) ).
thf(3024,plain,
! [A: $i] :
( ( b @ ( a @ implies ) @ ( A @ implies ) )
!= c ),
inference(simp,[status(thm)],[3023]) ).
thf(960,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= falsehood )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[628,206]) ).
thf(961,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[960]) ).
thf(962,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(pattern_uni,[status(thm)],[961:[bind(A,$thf( L )),bind(B,$thf( M )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( M @ ( L @ implies ) @ ( M @ ( K @ ( falsehood @ implies ) @ implies ) @ implies ) ))]]) ).
thf(1008,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[962]) ).
thf(1212,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[487,279]) ).
thf(1213,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) ),
inference(simp,[status(thm)],[1212]) ).
thf(1240,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) )
!= c ),
inference(simp,[status(thm)],[1213]) ).
thf(3360,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( falsehood @ ( D @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( F @ ( E @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3277,66]) ).
thf(3361,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( falsehood @ ( D @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( F @ ( E @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[3360]) ).
thf(3362,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( D @ ( falsehood @ ( E @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[3361:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( L )),bind(D,$thf( P )),bind(E,$thf( E )),bind(F,$thf( L @ ( falsehood @ ( P @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( I @ implies ) @ ( G @ implies ) ))]]) ).
thf(3388,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( D @ ( falsehood @ ( E @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[3362]) ).
thf(72,plain,
! [A: $i] :
( ( ( c @ ( a @ implies ) )
!= c )
| ( ( b @ ( a @ implies ) )
!= b )
| ( ( A @ ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[71]) ).
thf(11861,plain,
! [C: $i,B: $i,A: $i] :
( ( A != c )
| ( ( A @ ( C @ ( A @ implies ) @ implies ) @ ( B @ ( falsehood @ implies ) @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[10196]) ).
thf(11862,plain,
! [B: $i,A: $i] :
( ( c @ ( B @ ( c @ implies ) @ implies ) @ ( A @ ( falsehood @ implies ) @ implies ) )
!= a ),
inference(simp,[status(thm)],[11861]) ).
thf(362,plain,
! [A: $i] :
( ( A
!= ( c @ ( a @ implies ) ) )
| ( ( b @ ( a @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[270]) ).
thf(363,plain,
( ( b @ ( a @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[362]) ).
thf(498,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= D )
| ~ $true
| ( E @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[208,59]) ).
thf(499,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= D )
| ( E @ is_a_theorem ) ),
inference(simp,[status(thm)],[498]) ).
thf(500,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ implies ) @ implies ) )
!= ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ implies ) ) )
| ( A @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[499:[bind(A,$thf( F )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( K @ ( J @ implies ) @ ( K @ implies ) @ ( F @ implies ) )),bind(E,$thf( E ))]]) ).
thf(539,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ implies ) @ implies ) )
!= ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ implies ) ) )
| ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[500]) ).
thf(465,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( B @ ( D @ ( C @ implies ) @ ( D @ implies ) @ implies ) @ is_a_theorem ) )
| ( B @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14,60]) ).
thf(466,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( B @ ( D @ ( C @ implies ) @ ( D @ implies ) @ implies ) @ is_a_theorem ) )
| ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[465]) ).
thf(482,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ implies ) )
!= ( B @ ( D @ ( C @ implies ) @ ( D @ implies ) @ implies ) ) )
| ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[466]) ).
thf(3141,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) )
!= c )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3111,874]) ).
thf(3142,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) )
!= c ) ),
inference(simp,[status(thm)],[3141]) ).
thf(3143,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( falsehood @ ( E @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= c ),
inference(pattern_uni,[status(thm)],[3142:[bind(A,$thf( H )),bind(B,$thf( L )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( H @ ( falsehood @ ( L @ ( falsehood @ implies ) @ implies ) @ implies ) ))]]) ).
thf(3188,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( falsehood @ ( E @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= c ),
inference(simp,[status(thm)],[3143]) ).
thf(1758,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c @ ( a @ implies ) )
!= ( C @ ( B @ implies ) ) )
| ( ( C @ ( A @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( C != b )
| ( B != a )
| ( B
!= ( c @ ( b @ implies ) ) )
| ( A != a ) ),
inference(simp,[status(thm)],[1740]) ).
thf(1866,plain,
( ( ( b @ ( c @ ( b @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) ) )
| ( ( c @ ( b @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[1758]) ).
thf(1506,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= c )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1247,297]) ).
thf(1507,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= c ) ),
inference(simp,[status(thm)],[1506]) ).
thf(1508,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( D @ implies ) @ ( A @ implies ) )
!= c ),
inference(pattern_uni,[status(thm)],[1507:[bind(A,$thf( H )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( K @ ( J @ implies ) @ ( H @ implies ) @ ( K @ implies ) ))]]) ).
thf(1553,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( D @ implies ) @ ( A @ implies ) )
!= c ),
inference(simp,[status(thm)],[1508]) ).
thf(1274,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= c )
| ~ $true
| ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) )
!= falsehood ) ),
inference(paramod_ordered,[status(thm)],[95,297]) ).
thf(1275,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= c )
| ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[1274]) ).
thf(1276,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( D @ implies ) )
!= c )
| ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) )
!= falsehood ) ),
inference(pattern_uni,[status(thm)],[1275:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( C ))]]) ).
thf(29139,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1241,28616]) ).
thf(29140,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[29139]) ).
thf(29222,plain,
! [A: $i] :
( ( A @ ( A @ implies ) )
!= ( falsehood @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[29140]) ).
thf(2257,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1245,66]) ).
thf(2258,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[2257]) ).
thf(2259,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2258:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( D )),bind(E,$thf( M @ ( L @ implies ) @ ( M @ ( J @ implies ) @ implies ) @ ( J @ implies ) ))]]) ).
thf(2290,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[2259]) ).
thf(14742,plain,
! [A: $i] :
( ( ( c @ ( A @ implies ) @ is_a_theorem )
!= ( A @ is_a_theorem ) )
| ~ ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[14691]) ).
thf(12122,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( a @ implies ) @ is_a_theorem ) )
| ~ ( c @ ( C @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1395,11441]) ).
thf(12123,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( a @ implies ) @ is_a_theorem ) )
| ~ ( c @ ( C @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[12122]) ).
thf(12124,plain,
! [A: $i] :
~ ( c @ ( A @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[12123:[bind(A,$thf( a )),bind(B,$thf( E )),bind(C,$thf( E @ ( E @ implies ) ))]]) ).
thf(12235,plain,
! [A: $i] :
~ ( c @ ( A @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[12124]) ).
thf(15063,plain,
! [B: $i,A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( c @ ( B @ ( B @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14,12235]) ).
thf(15064,plain,
! [B: $i,A: $i] :
( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( c @ ( B @ ( B @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[15063]) ).
thf(15228,plain,
! [B: $i,A: $i] :
( ( A @ ( falsehood @ implies ) )
!= ( c @ ( B @ ( B @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[15064]) ).
thf(15942,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( falsehood @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ ( a @ implies ) @ is_a_theorem ) )
| ~ ( falsehood @ ( D @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3194,12356]) ).
thf(15943,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( falsehood @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ ( a @ implies ) @ is_a_theorem ) )
| ~ ( falsehood @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[15942]) ).
thf(15944,plain,
! [B: $i,A: $i] :
~ ( falsehood @ ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[15943:[bind(A,$thf( a )),bind(B,$thf( F )),bind(C,$thf( J )),bind(D,$thf( F @ ( falsehood @ ( J @ ( falsehood @ implies ) @ implies ) @ implies ) ))]]) ).
thf(16212,plain,
! [B: $i,A: $i] :
~ ( falsehood @ ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[15944]) ).
thf(1369,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1241,87]) ).
thf(1370,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) ),
inference(simp,[status(thm)],[1369]) ).
thf(1385,plain,
! [A: $i] :
( ( A @ ( A @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[1370]) ).
thf(9660,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( D @ ( A @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9053,279]) ).
thf(9661,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( D @ ( A @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) ),
inference(simp,[status(thm)],[9660]) ).
thf(9724,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( D @ ( A @ ( falsehood @ implies ) @ implies ) @ implies ) )
!= c ),
inference(simp,[status(thm)],[9661]) ).
thf(6684,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( B @ ( C @ implies ) @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) )
!= c )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14,608]) ).
thf(6685,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( B @ ( C @ implies ) @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) )
!= c ) ),
inference(simp,[status(thm)],[6684]) ).
thf(6686,plain,
! [B: $i,A: $i] :
( ( B @ ( falsehood @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= c ),
inference(pattern_uni,[status(thm)],[6685:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( falsehood ))]]) ).
thf(6831,plain,
! [B: $i,A: $i] :
( ( B @ ( falsehood @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= c ),
inference(simp,[status(thm)],[6686]) ).
thf(23860,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( C @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( C @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[3111,23207]) ).
thf(23861,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( C @ implies ) @ is_a_theorem ) )
| ~ ( C @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[23860]) ).
thf(23862,plain,
! [A: $i] :
~ ( falsehood @ ( A @ ( falsehood @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[23861:[bind(A,$thf( c )),bind(B,$thf( G )),bind(C,$thf( falsehood @ ( G @ ( falsehood @ implies ) @ implies ) ))]]) ).
thf(24096,plain,
! [A: $i] :
~ ( falsehood @ ( A @ ( falsehood @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[23862]) ).
thf(24154,plain,
! [A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( falsehood @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14,23735]) ).
thf(24155,plain,
! [A: $i] :
( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( falsehood @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[24154]) ).
thf(24333,plain,
! [A: $i] :
( ( A @ ( falsehood @ implies ) )
!= ( falsehood @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[24155]) ).
thf(3522,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( C @ ( falsehood @ ( D @ ( falsehood @ implies ) @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3274,279]) ).
thf(3523,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( C @ ( falsehood @ ( D @ ( falsehood @ implies ) @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) ),
inference(simp,[status(thm)],[3522]) ).
thf(3552,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( C @ ( falsehood @ ( D @ ( falsehood @ implies ) @ implies ) @ implies ) @ implies ) @ implies ) )
!= c ),
inference(simp,[status(thm)],[3523]) ).
thf(13485,plain,
! [B: $i,A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( c @ ( B @ ( falsehood @ implies ) @ implies ) @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14,12249]) ).
thf(13486,plain,
! [B: $i,A: $i] :
( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( c @ ( B @ ( falsehood @ implies ) @ implies ) @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[13485]) ).
thf(13637,plain,
! [B: $i,A: $i] :
( ( A @ ( falsehood @ implies ) )
!= ( c @ ( B @ ( falsehood @ implies ) @ implies ) @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[13486]) ).
thf(20840,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( E @ ( c @ implies ) @ implies ) @ ( D @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[61,14777]) ).
thf(20841,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( E @ ( c @ implies ) @ implies ) @ ( D @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) )
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[20840]) ).
thf(20842,plain,
! [A: $i] :
~ ( falsehood @ ( A @ ( c @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[20841:[bind(A,$thf( falsehood )),bind(B,$thf( G @ ( c @ implies ) )),bind(C,$thf( c )),bind(D,$thf( c )),bind(E,$thf( G ))]]) ).
thf(21005,plain,
! [A: $i] :
~ ( falsehood @ ( A @ ( c @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[20842]) ).
thf(2091,plain,
( ( ( c @ ( b @ implies ) )
!= ( c @ ( a @ implies ) ) )
| ( ( b @ ( a @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[2090]) ).
thf(2217,plain,
( ( c != c )
| ( b != a )
| ( ( b @ ( a @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[2091]) ).
thf(2218,plain,
( ( b != a )
| ( ( b @ ( a @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[2217]) ).
thf(286,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13,279]) ).
thf(287,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) ),
inference(simp,[status(thm)],[286]) ).
thf(300,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) )
!= c ),
inference(simp,[status(thm)],[287]) ).
thf(1585,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( D @ implies ) )
!= falsehood )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1469,429]) ).
thf(1586,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( D @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[1585]) ).
thf(1587,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(pattern_uni,[status(thm)],[1586:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( L )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( L @ ( L @ implies ) @ ( I @ implies ) @ ( G @ implies ) ))]]) ).
thf(1642,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[1587]) ).
thf(4670,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) )
!= c )
| ( ( C @ ( A @ ( C @ implies ) @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[3471]) ).
thf(280,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,264]) ).
thf(281,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[280]) ).
thf(283,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[281]) ).
thf(5796,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) )
!= c )
| ( ( B @ ( A @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[283]) ).
thf(16793,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ ( a @ ( B @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1241,16219]) ).
thf(16794,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ ( a @ ( B @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[16793]) ).
thf(16871,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( falsehood @ ( a @ ( B @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[16794]) ).
thf(9152,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9036,87]) ).
thf(9153,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) ),
inference(simp,[status(thm)],[9152]) ).
thf(9183,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[9153]) ).
thf(4456,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= ( c @ ( a @ implies ) ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[66,4127]) ).
thf(4457,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= ( c @ ( a @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[4456]) ).
thf(4458,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) ) )
| ~ ( D @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[4457:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( G @ ( F @ implies ) ))]]) ).
thf(4523,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) ) )
| ~ ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[4458]) ).
thf(23114,plain,
! [A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( c @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14,22675]) ).
thf(23115,plain,
! [A: $i] :
( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( c @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[23114]) ).
thf(23247,plain,
! [A: $i] :
( ( A @ ( falsehood @ implies ) )
!= ( c @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[23115]) ).
thf(3437,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3101,279]) ).
thf(3438,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) ),
inference(simp,[status(thm)],[3437]) ).
thf(3469,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ ( C @ implies ) @ implies ) @ implies ) )
!= c ),
inference(simp,[status(thm)],[3438]) ).
thf(377,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[334,193]) ).
thf(378,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[377]) ).
thf(400,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[378]) ).
thf(3130,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= falsehood )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3111,429]) ).
thf(3131,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[3130]) ).
thf(3132,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( falsehood @ ( D @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(pattern_uni,[status(thm)],[3131:[bind(A,$thf( G )),bind(B,$thf( K )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( G @ ( falsehood @ ( K @ ( falsehood @ implies ) @ implies ) @ implies ) ))]]) ).
thf(3196,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( falsehood @ ( D @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[3132]) ).
thf(1418,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= falsehood )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1395,429]) ).
thf(1419,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[1418]) ).
thf(1420,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(pattern_uni,[status(thm)],[1419:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( I @ ( I @ implies ) @ ( F @ implies ) ))]]) ).
thf(1473,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[1420]) ).
thf(9816,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9190,264]) ).
thf(9817,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[9816]) ).
thf(9883,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[9817]) ).
thf(5069,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( D @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4911,279]) ).
thf(5070,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( D @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) ),
inference(simp,[status(thm)],[5069]) ).
thf(5110,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( D @ implies ) )
!= c ),
inference(simp,[status(thm)],[5070]) ).
thf(307,plain,
! [B: $i,A: $i] :
( ( ( B @ ( falsehood @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[207,87]) ).
thf(308,plain,
! [B: $i,A: $i] :
( ( B @ ( falsehood @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) ),
inference(simp,[status(thm)],[307]) ).
thf(326,plain,
! [B: $i,A: $i] :
( ( B @ ( falsehood @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[308]) ).
thf(100,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13,87]) ).
thf(101,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) ),
inference(simp,[status(thm)],[100]) ).
thf(107,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[101]) ).
thf(338,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= C )
| ~ $true
| ( D @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[13,59]) ).
thf(339,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= C )
| ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[338]) ).
thf(340,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ implies ) )
!= ( B @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) ) )
| ( A @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[339:[bind(A,$thf( F )),bind(B,$thf( J )),bind(C,$thf( F @ ( F @ ( J @ ( F @ implies ) @ implies ) @ implies ) )),bind(D,$thf( D ))]]) ).
thf(358,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ implies ) )
!= ( B @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) ) )
| ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[340]) ).
thf(3161,plain,
! [B: $i,A: $i] :
( ( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3111,87]) ).
thf(3162,plain,
! [B: $i,A: $i] :
( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) ),
inference(simp,[status(thm)],[3161]) ).
thf(3177,plain,
! [B: $i,A: $i] :
( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[3162]) ).
thf(11963,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( falsehood @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ ( a @ implies ) @ is_a_theorem ) )
| ~ ( c @ ( D @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3194,11441]) ).
thf(11964,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( falsehood @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ ( a @ implies ) @ is_a_theorem ) )
| ~ ( c @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[11963]) ).
thf(11965,plain,
! [B: $i,A: $i] :
~ ( c @ ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[11964:[bind(A,$thf( a )),bind(B,$thf( F )),bind(C,$thf( J )),bind(D,$thf( F @ ( falsehood @ ( J @ ( falsehood @ implies ) @ implies ) @ implies ) ))]]) ).
thf(12252,plain,
! [B: $i,A: $i] :
~ ( c @ ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[11965]) ).
thf(2750,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) )
!= c )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[66,874]) ).
thf(2751,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) )
!= c )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[2750]) ).
thf(2752,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= c )
| ~ ( E @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[2751:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( H @ ( G @ implies ) ))]]) ).
thf(2783,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= c )
| ~ ( E @ is_a_theorem ) ),
inference(simp,[status(thm)],[2752]) ).
thf(1804,plain,
! [C: $i,B: $i,A: $i] :
( ( ( b @ ( a @ implies ) )
!= ( B @ ( A @ implies ) ) )
| ( ( C @ ( B @ implies ) )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ( C != c )
| ( A != a )
| ( B
!= ( c @ ( b @ implies ) ) )
| ( A != a ) ),
inference(simp,[status(thm)],[1736]) ).
thf(1829,plain,
( ( ( c @ ( b @ implies ) @ ( a @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( c @ ( c @ ( b @ implies ) @ implies ) )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[1804]) ).
thf(6188,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5885,87]) ).
thf(6189,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) ),
inference(simp,[status(thm)],[6188]) ).
thf(6209,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ ( A @ implies ) @ implies ) @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[6189]) ).
thf(21020,plain,
! [B: $i,A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( falsehood @ ( B @ ( c @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14,21005]) ).
thf(21021,plain,
! [B: $i,A: $i] :
( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( falsehood @ ( B @ ( c @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[21020]) ).
thf(21148,plain,
! [B: $i,A: $i] :
( ( A @ ( falsehood @ implies ) )
!= ( falsehood @ ( B @ ( c @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[21021]) ).
thf(67,plain,
( ( ( c @ ( b @ implies ) )
!= c )
| ( a != a ) ),
inference(simp,[status(thm)],[32]) ).
thf(68,plain,
( ( c @ ( b @ implies ) )
!= c ),
inference(simp,[status(thm)],[67]) ).
thf(9605,plain,
! [A: $i] :
( ( ( c @ ( a @ implies ) )
!= b )
| ( ( A @ ( falsehood @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[9604]) ).
thf(1901,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) )
!= c )
| ( C != a ) ),
inference(simp,[status(thm)],[1545]) ).
thf(1902,plain,
! [B: $i,A: $i] :
( ( a @ ( B @ implies ) @ ( A @ implies ) )
!= c ),
inference(simp,[status(thm)],[1901]) ).
thf(2655,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) )
!= falsehood )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[66,728]) ).
thf(2656,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) )
!= falsehood )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[2655]) ).
thf(2657,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood )
| ~ ( E @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[2656:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( H @ ( G @ implies ) ))]]) ).
thf(2699,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood )
| ~ ( E @ is_a_theorem ) ),
inference(simp,[status(thm)],[2657]) ).
thf(1340,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) @ ( B @ implies ) )
!= falsehood )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1241,429]) ).
thf(1341,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) @ ( B @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[1340]) ).
thf(1342,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(pattern_uni,[status(thm)],[1341:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( F @ ( F @ implies ) ))]]) ).
thf(1399,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[1342]) ).
thf(18972,plain,
! [A: $i] :
( ( falsehood != A )
| ( ( A @ ( falsehood @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[17744]) ).
thf(18973,plain,
( ( falsehood @ ( falsehood @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[18972]) ).
thf(596,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[61,8]) ).
thf(597,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[596]) ).
thf(607,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) )
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[597]) ).
thf(9101,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= c )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9036,456]) ).
thf(9102,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= c ) ),
inference(simp,[status(thm)],[9101]) ).
thf(9103,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= c ),
inference(pattern_uni,[status(thm)],[9102:[bind(A,$thf( G )),bind(B,$thf( K )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( G @ ( G @ ( K @ ( falsehood @ implies ) @ implies ) @ implies ) ))]]) ).
thf(9198,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= c ),
inference(simp,[status(thm)],[9103]) ).
thf(598,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ~ $true
| ( E @ is_a_theorem )
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[61,58]) ).
thf(599,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[598]) ).
thf(600,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ is_a_theorem ) )
| ( A @ is_a_theorem )
| ~ ( B @ ( C @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[599:[bind(A,$thf( H )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( K @ ( J @ implies ) @ ( K @ ( H @ implies ) @ implies ) )),bind(E,$thf( E ))]]) ).
thf(624,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ is_a_theorem ) )
| ( A @ is_a_theorem )
| ~ ( B @ ( C @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[600]) ).
thf(12273,plain,
! [A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( falsehood @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14,11895]) ).
thf(12274,plain,
! [A: $i] :
( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( falsehood @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[12273]) ).
thf(12412,plain,
! [A: $i] :
( ( A @ ( falsehood @ implies ) )
!= ( falsehood @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[12274]) ).
thf(11070,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,610]) ).
thf(11071,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[11070]) ).
thf(11072,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ implies ) @ ( A @ ( C @ ( B @ implies ) @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(pattern_uni,[status(thm)],[11071:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G @ ( F @ implies ) )),bind(D,$thf( G ))]]) ).
thf(11177,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ implies ) @ ( A @ ( C @ ( B @ implies ) @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[11072]) ).
thf(7257,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) )
!= falsehood )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[66,611]) ).
thf(7258,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) )
!= falsehood )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[7257]) ).
thf(7259,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) )
!= falsehood )
| ~ ( B @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[7258:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(7352,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) )
!= falsehood )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[7259]) ).
thf(2583,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[627,87]) ).
thf(2584,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) ),
inference(simp,[status(thm)],[2583]) ).
thf(2600,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ implies ) @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[2584]) ).
thf(979,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[628,279]) ).
thf(980,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) ),
inference(simp,[status(thm)],[979]) ).
thf(1004,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) )
!= c ),
inference(simp,[status(thm)],[980]) ).
thf(3422,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= c )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3101,297]) ).
thf(3423,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= c ) ),
inference(simp,[status(thm)],[3422]) ).
thf(3424,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( B @ ( D @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= c ),
inference(pattern_uni,[status(thm)],[3423:[bind(A,$thf( K )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( D )),bind(E,$thf( M @ ( L @ implies ) @ ( M @ ( K @ ( M @ implies ) @ implies ) @ implies ) ))]]) ).
thf(3474,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( B @ ( D @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= c ),
inference(simp,[status(thm)],[3424]) ).
thf(336,plain,
! [A: $i] :
( ( A != c )
| ( falsehood != a ) ),
inference(simp,[status(thm)],[284]) ).
thf(337,plain,
falsehood != a,
inference(simp,[status(thm)],[336]) ).
thf(1432,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1395,264]) ).
thf(1433,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1432]) ).
thf(1463,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[1433]) ).
thf(29455,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ ( C @ ( falsehood @ implies ) @ implies ) @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29046,66]) ).
thf(29456,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ ( C @ ( falsehood @ implies ) @ implies ) @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[29455]) ).
thf(29457,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( falsehood @ ( D @ ( falsehood @ implies ) @ implies ) @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[29456:[bind(A,$thf( G )),bind(B,$thf( K )),bind(C,$thf( O )),bind(D,$thf( D )),bind(E,$thf( G @ ( falsehood @ ( O @ ( falsehood @ implies ) @ implies ) @ ( K @ ( falsehood @ implies ) @ implies ) @ implies ) ))]]) ).
thf(29632,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( falsehood @ ( D @ ( falsehood @ implies ) @ implies ) @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[29457]) ).
thf(490,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) )
!= c )
| ( A != a ) ),
inference(simp,[status(thm)],[282]) ).
thf(491,plain,
! [A: $i] :
( ( a @ ( A @ implies ) )
!= c ),
inference(simp,[status(thm)],[490]) ).
thf(3199,plain,
! [B: $i,A: $i] :
( ( A != c )
| ( ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[3182]) ).
thf(3200,plain,
! [A: $i] :
( ( falsehood @ ( A @ ( falsehood @ implies ) @ implies ) )
!= a ),
inference(simp,[status(thm)],[3199]) ).
thf(1068,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) )
!= c )
| ( A != a ) ),
inference(simp,[status(thm)],[531]) ).
thf(1069,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) )
!= c ),
inference(simp,[status(thm)],[1068]) ).
thf(42229,plain,
$false,
inference(e,[status(thm)],[629,1469,11895,25531,23255,24108,6808,4183,628,9222,1549,730,9604,9383,13462,23455,9191,2363,11175,6830,873,3012,614,269,10,9184,5565,27683,8747,2448,7345,10940,6241,24134,16236,2360,8752,404,13975,2216,1243,1391,12763,12257,24131,5269,25,17428,1386,12356,1724,7343,23340,3195,14351,110,619,8753,542,12254,1628,14,1709,917,3485,2897,357,1462,6208,1545,3385,20,1247,1479,10945,3180,3268,14376,4788,1013,284,12392,9199,4368,3014,2024,12767,11441,2090,24137,1632,623,106,12436,4783,12236,821,16897,211,253,2291,1383,3290,3093,2964,1843,23069,2281,734,18578,2523,132,396,9341,428,5137,16219,9896,397,687,5220,61,12249,133,3184,206,24125,3186,9209,10922,1868,5122,25530,22877,23207,60,117,3303,15779,270,529,534,2296,9036,334,1387,12260,825,1021,2277,28,3022,1487,24120,429,729,23239,1238,3471,297,70,30567,693,9190,625,329,22046,2609,4187,461,13835,18315,456,285,252,1837,3269,361,65,1836,5113,1402,9196,874,5270,2359,1006,356,610,403,9,10203,4898,13434,9186,3179,23625,193,16201,686,23635,3194,212,109,328,3486,2519,29220,457,17096,24313,10894,622,837,2598,24112,9053,24758,13,4902,1246,12250,5112,360,4782,16220,1563,6812,1170,9213,14185,530,30555,23735,4288,1241,398,2368,298,1648,430,32,264,3289,733,1251,618,30542,14777,279,64,296,3111,3274,3187,1007,1388,13798,59,5271,12231,3472,875,16209,9210,17744,12401,611,7347,28616,1464,1638,540,71,12242,14743,12,29046,4127,4672,11201,9224,18309,831,30554,10204,736,9185,9723,616,3101,9344,7,7330,3197,434,3182,2896,208,14198,2871,1557,621,483,66,5885,12381,462,4911,609,915,6817,108,330,11173,399,5216,1245,1066,608,6816,299,267,2999,431,1562,1396,2439,30532,167,24314,17487,112,617,23696,1018,2597,2899,1551,9727,531,209,487,5133,458,12234,823,1845,1547,4366,4673,95,12390,327,16221,24093,1003,10196,63,282,1156,1267,4894,1637,331,3554,24247,1235,2276,16234,18307,359,24098,3095,6206,9194,613,2357,1485,11,3024,1008,612,1240,3388,72,11862,627,363,539,482,3188,14015,1866,1553,87,1276,12258,29222,2290,14742,15228,401,23,16212,1385,9724,6831,8,2081,207,24096,9211,24333,3552,13637,58,2362,21005,2218,300,1642,22675,4670,5796,16871,30,1395,9183,4523,19,23247,3469,210,3277,268,400,2091,3196,1473,9883,5110,326,107,358,3177,1561,12252,2783,283,1829,6209,21148,68,9605,1902,2699,1399,18973,607,9198,624,728,12412,11177,7352,2600,12220,1384,12235,1550,62,1004,3474,337,1463,29632,491,3200,1468,1069]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL030-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.13 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.14/0.48 % Computer : n001.cluster.edu
% 0.14/0.48 % Model : x86_64 x86_64
% 0.14/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.48 % Memory : 8046.5625MB
% 0.14/0.48 % OS : Linux 6.8.0-71-generic
% 0.14/0.48 % CPULimit : 300
% 0.14/0.48 % WCLimit : 300
% 0.14/0.48 % DateTime : Fri Sep 25 21:50:26 UTC 2026
% 0.14/0.48 % CPUTime :
% 0.14/0.48 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.99/1.06 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.28/1.25 % [INFO] Parsing done (182ms).
% 1.28/1.26 % [INFO] Running in sequential loop mode.
% 1.87/1.67 % [INFO] eprover registered as external prover.
% 1.87/1.68 % [INFO] Scanning for conjecture ...
% 2.09/1.76 % [INFO] Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ...
% 2.25/1.80 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 2.25/1.81 % [INFO] Problem is propositional (TPTP CNF).
% 2.25/1.81 % [INFO] Type checking passed.
% 2.25/1.82 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 145.14/38.79 % External prover 'e' found a proof!
% 145.14/38.79 % [INFO] Killing All external provers ...
% 145.14/38.79 % Time passed: 38173ms (effective reasoning time: 37527ms)
% 145.14/38.80 % Axioms used in derivation (5): c0_4, condensed_detachment, c0_1, c0_3, c0_2
% 145.14/38.80 % No. of inferences in proof: 1546
% 140.55/38.80 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 38173 ms resp. 37527 ms w/o parsing
% 147.72/39.17 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 147.72/39.18 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------